Yes perpetual stew is safe to eat.
When we think of perpetual stew we usually think that the perpetual stew is stew that has sat for awhile in the same pot.
However real perpetual stew is stew that is just made in the same pot over and over again with any ingredients that you have.
The pot is usually never or rarely cleaned out between cooking of the stew but you're getting fresh stew cooked in the pot and not old stew.
Now if the perpetual stew was old stew that sat in the pot for a few days and then reheated then it could be unsafe to eat.
But that's usually not the case as new ingredients are added as the perpetual stew is consumed.
Many people have survived on perpetual stew for thousands of years without any illness or other health issues.