Typically doctors/hospitals expect payment on the date of service. Medical bills will fall off your reports 7 years from the date of service. If you're filing for SSI then there isn't much they can do to you. But, if you're ever sued then you need to file an answer and then show up to the hearing to prove to the judge where your funds come from. For that type of debt they cannot take your money but if you fail to let the judge know you're on SSI then you might find your bank account frozen or the funds seized. If that happens you can always get it unfrozen or the seized funds back but it generally is a hassle and it takes awhile before you get your funds back. It's much easier just to show up for the hearing after being sued.
I'm not saying that they will sue, I'm only saying that if they do then your best interests would be to show up for it.
Also, if you do end up on SSI then there's no reason to file bankruptcy since you would be judgment proof. If you don't file bankruptcy and they don't sue then your reports will be clean after the time I mentioned above. If you file bankruptcy then your reports will be trashed and for a much longer time. If they file suit then there's the possibility of the judge dismissing the case because of your judgment proof status.
edited to add.
Just because a person is on SSI or SSDI does NOT mean that they can never get credit. Plenty of people that are on those programs are granted credit cards, car loans, mortgages, etc. It's still an income (a means of paying the bills) it's just not a 'working' income.