Firstly, if this individual is getting a government grant in cash, this might be considered income for the purposes of the bankruptcy, but since I don't know the specifics, it's hard to give an opinion.
There have been a few recent cases regarding an increase in the value of the property during bankruptcy generally. The trustee may require a new appraisal of the house, but that isn't a given. The bottom line is that if the work is done, more equity may become available to the creditors and the trustee is required to realize on that equity.
With respect to financing, this can be done via payments over a period of time, for example via a conditional order of discharge. If I recall correctly, the trustee can put a lien on the house and continue to take payments after the discharge.