Can a virus destroy the BIOS of a modern computer?
Modern computers don't have a BIOS, they have a UEFI. Updating the UEFI firmware from the running operating system is a standard procedure, so any malware which manages to get executed on the operating system with sufficient privileges could attempt to do the same. However, most UEFIs will not accept an update which isn't digitally signed by the manufacturer. That means it should not be possible to overwrite it with arbitrary code.
This, however, assumes that:
- the mainboard manufacturers manage to keep their private keys secret
- the UEFI doesn't have any unintended security vulnerabilities which allow overwriting it with arbitrary code or can otherwise be exploited to cause damage.
And those two assumptions do not necessarily hold.
Regarding leaked keys: if a UEFI signing key were to become known to the general public, then you can assume that there would be quite a lot of media reporting and hysterical patching going on. If you follow some IT news, you would likely see a lot of alarmist "If you have a [brand] mainboard UPDATE YOUR UEFI NOW!!!1111oneone" headlines. But another possibility is signing keys secretly leaked to state actors. So if your work might be interesting for industrial espionage, then this might also be a credible threat for you.
Regarding bugs: UEFIs gain more and more functionality which has more and more possibilities for hidden bugs. They also lack most of the internal security features you have after you have booted a "real" operating system.
Yes, it is definitely possible.
Nowadays, with UEFI becoming widespread, it is even more of a concern: UEFI has a much larger attack surface than traditional BIOS and a (potential) flaw in UEFI could be leverage to gain access to machine without having any kind of physical access (as demonstrated by the people of Eclypsium at black hat last year).
Practically speaking, a virus is software, so can do anything that any other software can do.
So the simple way answer to this question, and all others of the class "Can viruses do X?" is to ask "Does software currently do X?"
Such questions might include "can a virus walk my dog?" (not without a dog-walking robot); "Can a virus get me pizza?" (yes: this is regrettably not the main focus of most virus authors, however).
Are BIOSes (UEFI) currently updated using software? The answer is, yes they are. Mine updated last night, when I rebooted.
And so the answer is yes.
By the same logic, viruses can also cause (and historically have caused) physical damage to your CPU, hard drives, and printers.
Home automation systems and driverless vehicles are also possible targets for physical damages, but I know of no viruses which have done so.