Of course they can. Flash isn't a cloud service. All "deprecated" and "EoL" means is that Adobe isn't going to change the product or provide support. Google could do the same. It will keep working the way it has always worked. There's millions if not more sites out there still with Flash content. I have a collection of SWFs (mostly games) and they still work too.

The "this technology is old/deprecated/EoL/unfashionable/etc., let's just delete it all and provide no equivalent replacement, nevermind the fact that it's been working well" attitude is what really pisses off users, including me. Also somewhat like me, they don't really care what technology is as long as it works --- all they see is something which used to work is now broken and they can't do anything about it.