If the post is for instance older than 3 months and on page 10 or something you can just delete it since the odds of somebody looking at it is slim in the first place. This offcourse assumes that the requests are maneagable so that you won't get completely flooded. Another concern some people raised is that posters might get careless with personal information, I doubt this is going to be a problem unless you put in FAQ something like 'PM a mod to delete you post after 24 hours'. New posters probably don't know about the possibility of deleting posts and should assume that it isn't possible, this means that only the serious requests get through.
About the personal information, well its not very important for me but for some people its a really big deal and this forum is for helping not for sticking to rigid rules. Now I'm all for leaving it the responsibility in the posters hands but everybody makes mistakes at times and it can have some serious consequences.
Conclusion;
I'd say allow it unless it gets abused or its a important thread (like a 10 page 'post your picture thread' or 10 page 'post your contact information' thread). I'm sure the mods can deal with both exceptions.
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