The information you provide is inadequate to provide a platform for an intelligent answer, sorry. I want to help, but please keep in mind that presumptions are necessary to say anything meaningful. I am GUESSING that the home in which you currently live is in your dad's name as far as title goes. I do so because of the way you referenced his income in relation to its purchase.
Notwithstanding your father's identity as the home's buyer, you've stated that you funded the down payment, and that you make the monthly payments. Those facts may prove significant if your dad is currently incompetent and you end up in a legal disagreement with anyone defending your actions (see below). It would be wise to put together documentary evidence of payments by you together for sharing with the attorney I will recommend you hire.
I must confess that even reading between the lines, I can't piece together how the "other" home you purchased in Antioch fits into this puzzle. If I am correct in inferring that you own TWO properties in Antioch and the second one is also in your dad's name, you will likely need to take some action with respect to that asset as well.
In any case, the 800 pound gorilla of a question behind your question as posted is whether your dad is currently competent. A second major issue is whether you have other relatives (potential heirs of your dad) who are likely to challenge any actions that you've taken as self-serving and/or self-enriching.
If the property is in your dad's name, you can have competent legal counsel assist you in transferring it to a trust that benefits your dad for as long as he lives. What happens to the house, as long as it benefits your father, will "work." When your dad passes, if the trust still holds the house, it can pass (with almost all of his other assets) per the terms of the trust, to his identified successors. This will be a simple matter if your dad is competent AND you have no relatives who would like to be heirs of your dad's estate in your place.
The big "catch" is that if your dad isn't competent OR you have relatives who may make claims against you when they become aware of the estate planning discussed above, you had better dot all "i's" and cross all "t's" in setting up the trust properly. It may need to be a special needs trust or some other specialized estate planning vehicle. You may need to set up a conservatorship. Like the records of your payments for the house discussed above, a good handle on your dad's current health care providers, and a clear understanding of his medical condition will assist you in helping your attorney to protect you.
Be aware that people who do the sorts of things that you have done are often subject to allegations of financial elder abuse. In some cases, such allegations prove that many good deeds don't go unpunished. In other cases, the allegations are warranted and the "caretaking" relatives get the criminal charges and prison time that they deserve. PRESUMING that you fit into the former category, a good trusts/estates/guardianship attorney should be part of your immediate future plans. Sale of the house and/refinancing will be easy once the legal work I describe is done.
Your question's focus on the bank taking the house and the possibility of a refinance is a red flag for other issues. If a foreclosure is on the horizon, you may need to pursue a loan modification. Doing so if your dad is incompetent will make that process all but impossible if you don't get the trusts/estates/guardianship issues under control. Even if your dad is competent and you can proceed with the modification immediately, DO NOT hire and "pre-pay" an attorney or pay any lawyer advance fees if that ends up in your plans. Lawyers cannot legally collect advance fees for loan modification work. If a lawyer helps you with loan modification, that lawyer can only gt paid by you once the modification goes through.
Adding categories to your question!
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There is not a lot to add to the excellent answer above. If title is in his name, no, you cannot sell it because you do not own it. If your name is not on the deed and he agrees it should be, you need to change that while he is able to do so. An alternative is to have him sign a document setting out your financial rights if any to the property. I too do not see what the rental home of yours has to do with this. What I do know is you need to see an attorney now to resolve these issues before you lose your opportunity.
If you liked this answer, click on the thumbs up or vote it best answer! Thanks. Eliz. C. A. Johnson Post Office Box 8 Danville, California 94526-0008 Legal disclaimer: I do not practice law in any state but California. As such, any responses to posted inquiries, such as the one above, are limited to a general understanding of law in California and not to any other jurisdiction. In addition, no response to any posted inquiry should be deemed to constitute legal advice, nor to constitute the existence of an attorney/client or other contractual or fiduciary relationship, inasmuch as legal advice can only be provided in circumstances in which the attorney is able to ask questions of the person seeking legal advice and to thus gather appropriate information.
The first issue is how is title held to the subject property in Antioch? In your Dad’s name ir your name or both names or in a trusts’s name or in some other form? Someone will have to look at the vesting deed as well as your father’s will and trust if he has the same to give you an answer.
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From a purely real estate perspective, if you hold title as "Joint Tenants with Rights of Survivorship" or just "Joint Tenants" then when your father passes, the title automatically is in your name alone. If your not also a co-borrower, the lender may call in the loan in which case you should have time to either re-finance or sell.
All of the other issues from the estate planning attorneys above are also issues to evaluate with your own retained counsel where you can confidentially evaluate your risks vs. costs.
Kevin A. Spainhour, Esq. Spainhour Law Group www.slglawyer.com.