If it is a properly done mod why not grab it and trade it with someone for a clean one if you really want one of those (I don't know why you would at this point, not like 360 xbox live is something worth having)?
Ignoring boring mods then there are two classes
1) DVD mod and ODDE. Can play copied games but only in region and unmodded.
2) JTAG/RGH/SMC/KK family. These will do things like allow it to run from internal hard drive (which can be made as large as you like), out of region games, modded games, cheats, USB launcher, controller remapping, DLC, XBLA games, homebrew and more besides.
If it is 2) then they are not necessarily a rare and precious commodity but it would be a shame to destroy one.
Do also try to find out what motherboard type it is
https://gbatemp.net/threads/found-a-360-worth-it.458746/#post-7044412
Nothing older than Jasper for me at this point. If you do then you play the RRoD gauntlet.