Hydrides and alkyl groups often shift in E1/SN1 reactions. Can you have a concerted shift in an SN2/E2 reaction?
no, that would complicate the interaction between atoms during the concerted reaction too much and make it unlikely to happen.
e1 and sn1 reactions proceed via a carbocation intermediate. The reason you get these shifts is because after the formation of the carbocation a lower energy configuration can exists without the input of extra energy (a 2 prime carbocation will become a more stable 3 prime carbocation). E2 and sn2 reactions occur via a one-step mechanism so there is no need for a shift. The molecule never exists as a less stable carbocation so there is no driving force for rearrangement.