Dry dog and cat food will be the last items off of the shelves, along with the drier canned pet foods.
There are only 3 days of supplies in American Cities' store shelves at any given moment.
It normally takes 3 hours for the "unprepared" to clean out the store shelves when a forecasted event (severe storm, hurricane, etc) warning has been issued.
It takes about 3 to 7 days (normal times) for the stores to order, receive, and restock the shelves.
After an event has come and gone, it'll take more like 7-14 days for supplies to make it from the time of the order being placed, to the shelves being restocked. There will be communications problems, computor problems, fouled roadways, etc; that will add time (days) to the process.
My personal opinion: By the time the "prepared" need to resupply, there will not be any dog or cat food left on the shelves.
Military (National Guard, USCG, etc.) and civilian (Salvation Army, Red Cross, local Churches, etc.) organizations will have become established on scene, providing food (MRE's, hot coffee, etc), clean drinking water (bottled and tanked in), porta-potties, emergency shelters (public buildings, tent cities, or the newly planned "Containerized Family Shelters"), Emergency Medical care (Military and civilian), Law Enforcement (including anti-sniper teams), etc, etc, etc......
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QMC, USCG (Ret)
The best luck is what you make yourself!