The resizing of the / var directory was achieved with the Gparted live CD due to the urgency I had in executing the process, however, while waiting for the Gparted .iso it occurred to me to try to resize the partition "live". To complete this task I read that I had to disassemble first / var.
It happens that I tried to disassemble / var but the system threw me a message that said (words more, words less) that there was a running process in / var and when it was busy the dismantling could not be performed.
I was in charge of researching and I did not find a concrete and convincing explanation of why / var can not be dismounted from the same operating system in which it is currently running, so I decided to try it.
I rebooted the machine (so as not to have any additional process that would prevent me from executing the process) and forcibly disassembled / var through the terminal. The machine in response to my action generated a "blink" visible on the monitor, I clarify that it was not rebooted because when the screen turned on again it did not boot but asked for a username and password as if it were returning from a state of suspension or hibernation.
Then I had doubts about everything mentioned above. These doubts are:
1) Is it possible to resize "live" or "hot" / var?
2) Why did my machine "blink" when disassembling / var forcibly?
3) Which processes do you manage are important enough so that try to disassemble / var the system I threw the message that I mentioned previously?
4) Why being so important at the programming level (among other things) the folder / var the system (Debian for example) in its installation process to perform a "guided" partitioning provides a space so infimo in comparison to the entire disk? Is there a special reason for this?
Observation: I know that / var is a reference for certain services associated with web development (Apache, docker, among others) but I do not think they are the ones that generate this problem since there is no "resistance" of the system when stopping these services per terminal.
Observation 2: I have read many forums and technology sites but they do not explain for sure a convincing reason for each of the doubts raised and I am one of those who likes to understand as best as possible each process, tool, etc.
I thank you in advance for all the help provided.