I don't get here much in these other drawers but I found this on Ancestry-not sure if this is your guy but here it is.
Name: Richard H Cullen ,
Residence: Assabet, Massachusetts
Occupation: Marble Worker
Enlistment Date: 19 February 1862
Side Served: Union
State Served: Massachusetts
Service Record: Enlisted as a Private on 19 February 1862 at the age of 18
Enlisted in Company F, 32nd Infantry Regiment Massachusetts on 19 February 1862.
Reenlisted in Company F, 32nd Infantry Regiment Massachusetts on 01 January 1864
Mustered out Company F, 32nd Infantry Regiment Massachusetts on 29 June 1865
Source Citation: Side served: Union; State served: Massachusetts; Enlistment date: 19 February 1862..
I did find a pension request from a widow Bridget Cullen but honestly there is virtually no information on the card beyond that. I have done Civil War research at the National Archives and even got to look at the original documents. It is interesting to say the least but not much there beyond what you see here.
I had a long conversation with one of the caretakers there-I was hoping to discover more personal information and what I was told was that that kind of information was not usually recorded because (to answer my question -what if someone was killed-where and who did they know to notify) that most came from the same town or area and the regiment was kind of a small town-everyone knew everyone and their families. Well that was the response I got.