When I close an assembly,  a window with one of the parts remains.

Is there any chance that that Part was inserted into another Part in the Assembly?  I've had cases where the inserted Part would open anytime the Part it was inserted into, or an Assembly it was used in, was opened.

I see this fairly often.

I work a lot with split parts/assemblies.....I'll draw several bodies in one part file (typically weldment profiles).. then use the "save bodies" command to create individual part files for the bodies & a related assembly.   Then, when I open one of the new split parts or an assembly containing a split part, sometimes the original part file is also opened... 

I don't know if there is a way to control this behavior, or why it seems somewhat inconsistent.  At any rate, its not too annoying.. just be sure you don't start editing the wrong file!

Is it a "Read Only" file??