Downloading an older non-compatible Mac OS to create bootable disk for an older Mac that has crashed.

To perform this action will require booting from a Bootable Installer. 

The Bootable Installer can Only be performed on an Apple Computer 

This will have to be performed from a Qualifying Computer to run the version of macOS to be made on the Bootable Installer. Example : Bootable Installer of Big Sur would have to be done on a computer that Qualifies to run Big Sur.

Notation: If the computer being used to perform this action is Too New or Too Old to qualify to run the version of macOS - this computer can not be used.

Alternative is, to gain access to a Qualifying Apple Computer from a family member, friend or associate.

What do you mean by "died? Died implies a hardware failure. It would help to know more specific details here.

What is your goal here? To recover data from the older computer that crashed? Are you planning on reinstalling macOS over top of itself on that computer? You do realize this may put your data at risk even though in theory reinstalling macOS over top of itself should not affect the data under normal circumstances.

If your goal is to recover the data and you don't have a backup (why no backup?), then it would help to know the exact model of this older Mac that has crashed so we can provide some other options to access the data. You can get this information by entering the system serial number here:

Check Your Service and Support Coverage - Apple Support

Without knowing the exact model of the older Mac, the best we can offer at this time is to put the older Mac into Target Disk Mode and connecting it to your newer Mac in order to attempt to recover the data.

If the older Mac uses a hard drive, then that hard drive may be failing. If this is the case, then the more you use the drive (even having it powered on) and the more you attempt to recover the data, the more likely the drive failure will get worse where even a professional data recovery service may be unable to recover any data. Proceed carefully if this is the case as you may only get one chance at recovering your data.

You can use the following article to find a Qualifying Mac as it shows which versions of macOS are compatible with various Apple hardware:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

On what Mac would you be running it on?

Do you have a Time Machine drive the old one you could move over to the new one>