Pets left at home

Leave them plenty of food and water before you leave.  
I'm not sure where you're going with this.  Are you asking if there was a way to check on them if you are stuck in the hospital?  Like an indoor camera?  Or are you looking for some kind of automated feeding/watering system if you are stuck away from home for an extended period of time?  Perhaps you can be a little more specific about what you are hoping for.

Yep, I'd definitely like to hear more about what kind of scenario we're talking about here. As mentioned, an Indoor Camera can be helpful for keeping an eye on your pets to make sure they're okay.
If you have friends or family nearby (or maybe a neighbor) you can give them their own PIN for the security system, and if you have a Smart Lock, they'll be able to let themselves in without having a key. So they can check in and make sure that your pets are taken care of if you need to be away for longer than expected.

- Johnny M.
SimpliSafe Home Security

There are automatic (timer based) feeding and watering devices.  Use them all the time and keep them filled, and they will take care of any unplanned/extended absences.  Won't help with them going out, though.  Doggie door perhaps, with an alarm sensor set to secret alert and with a camera pointed at it.

Or you could make arrangements with a friend or neighbor to step in if you don't contact them by a certain time.

Sorry, there is absolutely no way for an alarm system to know that you were in an auto accident.  And there is no way an alarm system could activate any kind of pet care.