1 I created 2 precompiled DLLs through VisualStudio: DLL2 references DLL1
2 I drag and dropped those DLLs to Unity project
3 I created a script that uses classes/methods from DLL2 and added that script to a GameObject in the scene
4 Press Play - everything works
5 Stop Play mode
6 Delete DLL1
7 Now there are errors:
"Assembly 'Library/ScriptAssemblies/Assembly-CSharp.dll' will not be loaded due to errors:
Reference has errors 'Dll2'."
and
"Assembly 'Assets/Dll2.dll' will not be loaded due to errors:
Unable to resolve reference 'Dll1'. Is the assembly missing or incompatible with the current platform?
Reference validation can be disabled in the Plugin Inspector."

Actual Results: You can "Clear" those errors from the Console and they are gone, you can press Play and it enters Play mode
Expected Results: in my opinion those are kind of "compile errors" and they should be treated in the same way ?

How can we reproduce it using the example you attached
1 Open attached project (New Unity Project_dll_a16.zip)
2 Go to Project Browser and delete DllTest.dll
3 Press Play

Actual Results: there are 2 errors appear but you can "Clear" those errors from the Console and they are gone, you can enter Play mode
Expected Results: in my opinion those are kind of "compile errors" and they should be treated in the same way ? - meaning Play mode shouldn't be allowed and errors can't be "Clear"-ed from the Console