exosomes，you mean not cells just the objects like beads with  MHC?  

T cell not only bind MHC but also the  second signal （CD80, CD86……) , Which are used to silence the T cells.------"Control of peripheral T-cell tolerance and autoimmunity via the CTLA-4 and PD-1 pathways"

However (B cell) the antibody will targets it (If there is antibody).