The other week, I wrote about complementarianism and singleness in response to the claim that Complementarianism gives no space for single women in the church or society because women are required always to relate to God and others through the authority of a man. In that article I explained that this is a misunderstanding of what complementarianism is because the word simply provides a label to how we interpret a number of verses including Genesis 1:26-28 and Ephesians 5:21-32 and apply them specifically to husband and wives and then to the role of elder within the church. Complementarianism does not claim to be an overarching system for how we are to apply the whole of Scripture to every aspect of life. So, the follow up question you might be asking is “What then do you think Scripture teaches about single people whether they have never married, are divorced or widowed?
Well, here are the key Scriptures and my understanding of what they are saying.
To Single People
In 1 Corinthians 7:8 Paul says:
“8 So I say to those who aren’t married and to widows—it’s better to stay unmarried, just as I am.”
Now, it is important to observe at this stage that Paul is not denouncing marriage. We know that the place of marriage and family life plays a central part in his theology and understanding of the Christian life. Furthermore, notice in verse 26, that Paul is writing to a particular context. “Because of this present situation.” What that situation is, he leaves tantalisingly open though the common view is that he is referring to a specific crisis within Corinth, perhaps that of famine, distress and plague. So, the circumstances call on people to “remain as they are.” This means single women should stay single (v26). This is advise not an infallible command from the Lord (or possibly the point is tha the is not drawing from the actual words of Christ in the Gospels here).
Meanwhile, this is no chastity or purity cult/movement. Paul says that those already married are not to abandon their marriage vows, nor to deny each other sexually. Furthermore, there will be some who need to get married because they will not be able to control their passions and desires otherwise here. I believe in the context of wider Scripture that this is not just the offer of marriage as a way to put a lid on lust generally, rather, it will be that there will be a right desire for a woman and man who love each other for each other physically and that therefore, they should seek to get married.
The important thing is that Paul sees singleness as positive, something appropriate for certain contexts, a gift from God and something that he can commend because he too is single. Again, when we describe singleness as a gift, I don’t believe that Paul is meaning that if you are single and called to singleness for life that you suddenly will be equipped with a removal of loneliness or sexual desire. The gift is the singleness itself, the life situation you find yourself in that God has called you to. Your singleness will give you freedoms and opportunities to serve with your gifts that may not be as available to married people and families.
In that sense I want to argue that both marriage and singleness are gifts to the church as well as to wider society. We might expect from Scripture that marriage and children is the more common pursuit in life but that does not reduce or remove the value and worthiness to a calling to remain unmarried or the value and dignity of those who through desertion or widowhood find themselves single again.
The key passage here is 1 Timothy 5. It is worth noting that Paul instructs Timothy, a young pastor on how to treat women generally first. He is to treat older women as he would his mother and younger women as though they were his sister. This points to courtesy, respect and care and not to him lording it over them. 
Paul then goes on to give instruction for the care and treatment of women. Notice that he distinguishes between those widows who are likely to need care and support due to the frailty of age and those who will not, the younger widows. Younger widows are not to be given a place on the widows list (i.e. to receive financial and practical support from the church). This is because Paul does not want to encourage a dependency culture. The younger widows are at risk of breaking a pledge if they remarry suggesting that their place on the widow’s list involved a vow or commitment, a role in the life of the church. They are not to be bound to this commitment too soon. They are free to remarry but also the sense is that they remain at a stage in life where they should be able to play an active role in society, to pursue their vocational calling and to provide for themselves.
Meanwhile, the older widows are to be provided for but there are conditions. They are to demonstrate a commitment to Christ, a spiritual concern. They have put their trust in Christ and so give their time to prayer. Notice that they are expected to have godly reputations as faithful, just as similarly are the elders in the church. Indeed, we might look to them as the “spiritual mothers” within the church family. This is further supported by two other things. First of all, that the church family is now their only family, that no-one else has responsibility for their care, note too that women are to take responsibility for the care of other (widowed) women. 
Furthermore, we know that Paul expects women to take spiritual responsibility for other women. If the primary purpose of submission and authority in the NT is to do with teaching and discipleship, then young women (single or married) are not so much explicitly instructed to submit to men apart from their husband as they are to older godly women. This suggests to me that this is the spiritual calling of the widows. Here is Paul in Titus 2:3-5.
3 Similarly, teach the older women to live in a way that honours God. They must not slander others or be heavy drinkers.[a] Instead, they should teach others what is good. 4 These older women must train the younger women to love their husbands and their children, 5 to live wisely and be pure, to work in their homes,[b] to do good, and to be submissive to their husbands. Then they will not bring shame on the word of God.
Scripture values the place and the role of single women in the church including those who have become single through widowhood. There is of course mutual submission and single women are expected to submit to the elders but in no different a manner to how men and married women should submit.
 1 Timothy 5:1-2.
 1 Timothy 5:11-15.
 1 Timothy 5:3-10.