UPDATED 2021-03-21 Added New Diagnostic Information and Updated Title The problem still occurs and appears to be a serious issue with the elementary OS custom file dialogue component.
UPDATE I thought this group was for bug reports. I was wrong. Now I moved the bug report to the bugreporting lists on GITHUB. See https://github.com/elementary/applications-menu/issues/468 For other users, elementary OS maintains a separate Bug Reporting system via GitHub (not this stackexchange group). See https://elementary.io/docs/code/reference#avoid-subjective-or-ambiguous-adjectives for a detailed list to report bugs to the bug system, not support system (as is stackexchange). Bug reporting tool via System Settings...Info...Report a Problem.
The crashing appears intermittently but frequently. I ammnd the original report below to indicate that the issue applies to more than just web-based PDFs. for example, the crashes occur when saving a document created in LibreOffice Writer.
Summary Attempt to save a web-based PDF results in an immediate crash of the web browser/PDf viewer. Cannot SAVE web PDFs. Occurring for at least a month.
System Info elementary OS 5.1.7 Hera (updated to 2021-03-16) any web browser (Firefox 86.0 x64 or Chromium Version 89.0.4389.82) System Memory 32GB
Description Open a website using any web browser. Identify a PDF. Select the PDF. The browser (example Firefox) opens a dialogue window: What should Firefox do with this file?. Any attempt to SAVE or SAVE AS the file results in an abrupt and immediate crash of the web browser.
Similar situation in Chromium. PDF opens in Chromium but any attempt to SAVE results in a sudden and immediate crash.
Effect Cannot use elementary OS to save web-sourced PDFs.
I thought that this might be a flatpak issue. I did
flatpak list and NONE OF THE BROWSERS are installed via flatpak (they do not appear in the list). The browsers are default apt package manager/appcenter installations.