i decided to build an apartment, and after a few days i completely build and furnished 4 apartments. but when i want to move in a family, the apartments are unfurnished. so i took a look at furnished apartments already standard in the game. with this i had the same problem, everything was suddenly unfurnished when a family moved in. is this an error or something? or have i just completely wasted time decorating every apartment...

This is standard game behavior. You need to use a cheat to keep the furniture. Check out the section entitled "Renting Furnished" here:
Tutorials:Building_an_Apartment^wiki