I assume you are referring to a survivalist scenario....
You will have major problems with vermin and would have to clear and dispose of all perishable goods within a very short period otherwise you will have serious health risks with disease and infestations.....also most supermarket structures have very short term lifespan, around 10 years or so, needing major refits on a regular basis.
They would also be high value targets to just about any roving band of survivors so would need to be in an easily defensible position (which they rarely are) with the required manpower to do so, which in turn will drain the resources of the supermarket that much faster.
Without significant power and heating, clothing and dry goods would soon succumb to damp and mold, not to mention the aforementioned vermin issues.....
And that is just stuff I can think of on the spur of the moment.
Supermarkets are not ideal places to hold-up....they should be treated as potential resupply only and even then with great care and planning, otherwise they should be avoided wherever possible.