Hmmm... I had only loosely noticed that sometimes the items I left on the shelf were gone, so that's good to know. Do you have Get to Work? If so you could maybe try putting the Lice Cold Freezer (which does not sync with the refrigerators) on the lot, and drag them to the freezer when you leave the lot? I just re-visited a lot I with a home bakery/business have not played in a while while playing other households in the save and I see that the non-food items and produce I had left on the display shelves; and the produce, fizzy juice, and candy items I left in the 'display coolers' are still there, but not the prepared dishes and baked goods. However, the items in the freezer are still there. It may be useful to note that though the items are in an area designated for the small business I have since then moved the sim that owned the bakery to another lot, so there is no small business owned by any of the sims left on the lot.
So... I went to another lot with a home business with the owner, filled the displays, opened the business, saved and left the lot with the business open. Then I went to a sim of mine who was a neighbor and she was able to visit the lot and could eat an apple from a display shelf and a sale ticket animation happened (but I'm not sure she was charged for it), but she did not have an option to purchase from the display cooler, though she showed options to interact with the meals/baked goods there items in the cooler display. In regards to the meals/baked items in the cooler display, she could not 'put away' (she showed a blocked thought bubble), but she could 'throw away', to which she grabbed the item as trash and headed off somewhere off-lot to throw it away. Weirdness. Anyway, the food items were still there for now, but they had not been left for long. The business was still open when I went back to the owner. So kukkahilla it looks like your other sims may not be able to shop from it normally if you leave the lot/owner? However, I'm not sure how long it may take for meals/baked items to be gone from the shelves, but it looks like it didn't happen right away. They were also still there after I closed the game and re-entered the save. On both lots, though, I did find that the items I left in the Lice Cold Freezers were still there, and these items were made and stored in the freezers for maybe close to a rl year.