Is it possible to write to the hdd a file that does not have enough space?

Question

Hard disks

Can files be written to the hard disk if there is not enough space left?
What happens if one of the hard disk partitions is full, and a file is automatically loaded onto it?
What will happen when the hdd completely runs out of space and is this possible?
P.S. for those who can not understand the essence of my stupid question. I myself do not understand what happened to my hard drive on my laptop. It was Windows 7 basic, one partition d was completely filled, and the partition half. The virus is excluded, because there was a good antivirus and a browser with protection. One fine day, when the system was booting, a BIOS message began to appear stating that there were bad sectors on the disk. I trusted the programs for hard, they did not reveal any problems. Marvelous! I took the disk to the SC for verification, they checked nothing. I brought it home, installed it, formatted it clean and started installing the OS. The installation was successful and subsequent downloads no longer gave messages about bad sectors. I sin on Windows with its obsessive and hidden installation of dozens. Paranoia?