A resulting trust occurs where one person deeds the property to another with the understanding that the new owner will be an owner in name only. This may be what you have here. But the new owner is, of course, entitled to compensation for the service. This situation can be resolved by mutual agreement reduced to writing or through the courts. Consult an attorney.
Not clear as to the question. Who deeded the house to your husband? How long ago? Are you saying the "man" lived in the house rent free and now wants money on top of that too?
I agree with Mr. Graham.
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I have read your question and comments. The situation is too complex for an answer through this forum. Your husband needs to consult an attorney. There are many issues which need to be considered along with the exact facts, including the terms of any agreement between your husband and "the man." Good luck.
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After reviewing the questions and comments there still appears to me missing information. Mostly, how much was paid off, what was the value of the home at each relevant time, how much was invested in the renovations, and how much of the rents does the previous owner expect?