Updates after EOL

Up to the last released updates for that version, yes. But there won't be any new patches after the EoL date.
 
It is better to "port" whatever you are running on that old EoL version of FreeBSD to a supported version if you care about updates, IMHO.
 
If it's some specific binary, or something for which the source may not be available, for a particular FreeBSD version there's also the various compat* ports/packages. And the COMPAT_FREEBSD# options in the kernel (the GENERIC kernel supports all the way back to FreeBSD 4).
 
Up to the last released updates for that version, yes. But there won't be any new patches after the EoL date.
Some days ago I tried to install program with "pkg" on FreeBSD 12.4 without success. It seems ports library is not online for EoL versions. From this topic I had the belief that I can install EoL version and add all necessary packages (until their last update).
 
It seems ports library is not online for EoL versions.
Ports are in git, it's a version control system and allows you to jump back in history. You're talking about packages and specifically the FreeBSD package repositories, those are indeed gone because package repositories for old, unsupported, versions aren't kept around. There is an archive but this only contains packages for the stuff that was on the DVD images when that release was made.

Patches for the base OS are still available through freebsd-update(8) (or git checkout of the source). Up to the last patch that was created for that old version.
 
(Edit: SirDice beat me to it :) )
The important distinction here is between the ports repository (=the ports tree) and packages (in the package repositories) that are currently build and supported on the FreeBSD remote servers.

Packages for supported branches (13 and 14 at the moment) are build only for certain architectures; and in two varieties: "latest" and "quarterly". When you want packages other that what is offered, you can download the source of a specific port from the ports tree (and all of its dependencies) from a specific time relating to the desired FreeBSD version and build it yourself. However, that comes with possibly a lot of overhead: see for example Is v13.0 still usable?
 
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