MySQL will not run after exhausting disk space while indexing
There could be about 3 things going on here...


You ran out of disk space.  Can you scrounge some space, even a little?
You cannot connect because of a socket problem.  Remove the socket and try again.
The attempt to add an index could have been performed in a couple of different ways.  Was the table MyISAM?  Or InnoDB?  If InnoDB, was innodb_file_per_table ON?


In any case, look for #sql... files they were the tmp tables being built before "renaming" them into place.  They are useless no; remove them.

If file_per_table was off, then probably ibdata1 got a lot larger in this failed operation.  This will call more a messier repair.

Since you have an old version of MySQL, I won't point out ALTER TABLE .. ALGORITHM=INPLACE, ADD INDEX ..;