As someone who is sitting on over 1000 mods I can tell you the cap thing is pretty annoying.
I've had to level up a huge amount of characters to level 50 just to equip mods. Currently I have 522 mods on all of my characters that can equip them. I counted my inventory last week and I have I believe 590 or it was 490..cause I kinda lost count.
Anyways what happens when you reach the cap is that they go into your mailbox. You won't beable to put them in your inventory or on a character until you make room..by either lvling a character to 50 or until you sell them.