Plumbing: How to remove remaining piece of nipple from galv elbow

Need a little help here...
Undersink plumbing. Drainage Piping... The nipple which goes into the wall, corroded and broke off flush where it goes into the Elbow. Are there any methods for removing the remaining piece in the L. I'm a little cautious about attempting to replace the L, reason being that I'm not sure of the condition of the rest of the drainage pipe. This is in a 35 y/o condo.
If I had to replace the Elbow, can I just use the solvents available at auto stores to remove rust or are there special rust breaking solvents available??
Thanks in advance for your help....
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