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solaris 8 permits logins, etc. to a machine with full partitions.
even with only 1 partition, logins are permitted.
of course, no writes can take place.

solaris eventually takes control of all the swap space and distributes
as needed to processes.  free swap space, over time, will be reduced
normally.  (there are posts in the archives about swap and how the os
manages swap.)

the full file system would not cause the problem you discribed though
you should check for memory leaks, etc.