It's difficult to comment, as there's not really enough information in the OP.
Your daughter has sold her house. Why?
They have nowhere to live now. Why?
Your son in law has serious financial problems in the past. From what?
He concealed these difficulties. Why?
Does his financial past mean they can't now get a mortgage, or won't be accepted for a rental agreement?
Your son in law hasn't ventured an opinion as to whether he wants to move in with you? Why? Has he been consulted, or have you and your daughter made this decision?
Your house is small, you say. How small? Is there physically enough room for you all? Can your home accommodate four additional people?
Where will their belongings be - are they bringing those with them, or putting them into storage?
The most concerning part of the OP, because of lack of information, is the "other aspects of his behaviour". This could be anything from alcohol misuse or drug misuse to coercive control of his wife and/or children. Would you be comfortable for these behaviours to continue in your home?
You say you wouldn't want much of a financial contribution, but have you actually considered how much having four additional people in your home will cost? Additional heating, lighting, water, food? I understand it would be uncomfortable taking money from them, but to be honest, you don't want to make them too comfortable, and not want to move on.
wellbeck has made some good points in the post above.
I would be very wary of having them move in with you, unless everything is agreed and put in written form. And even then, I personally would be saying "sorry, it's just not feasible".