Hello, thank you for using this service. My name is ***** ***** I am a licensed California attorney. I will be helping you with this question, but please understand that I can only provide you with general information in this forum.
Now, I first want to tell you how sorry I am about your boyfriend. In probate, your boyfriend's estate will be administered and, after payment of valid debts, distributed to his heirs. Because you were not married, you are not an heir and instead that will be his son. How long you are able to live in the house depends on a number of factors. Generally, the administrator will be the one who decides how long you can stay in the house while the estate is being administered. The heir will somewhat have a role, but it will be up to the administrator to decide if the house can be maintained or if it will need to be sold. If you have a good relationship with these people, then they may be willing to let you stay in the house and pay rent. If they need to sell the house, either because they can't afford the mortgage or they need to pay your boyfriend's debts, then you may not have a long time to stay in the house. It will take a few months to get a court order to sell the house, so you will probably be able to stay there during that period. However, I expect a court would allow the administrator to sell the house if it is necessary, which would consequently require you to be out of the house. You may, however, be able to stay in the house while it is on the market.
Second, how old is the son? If he can't manage the property, the court could put the house in a constructive trust. If you were paying rent or part of the mortgage that could provide some grounds for you to claim that you were a renter and thus entitled to more rights in regard to being forced out of the house. But, at the end of the day, you unfortunately don't have any strong rights that you could enforce. It all really depends on your relationship with the administrator and your boyfriend's son or other heir that the court determines should inherit the house.