From "ALPA's Guide to FAR 117":

Q-74. Can the certificate holder require a flightcrew member to check a computer, email calendar, text or other conversation media to determine assignment, changes, etc. during a rest period?
A-74. No. During a rest period, regardless of length, a flightcrew
member must be free from all restraint. If a flightcrew
member is required to do something by the certificate
holder, he/she is not free from all restraint.

Q-75. Could a flightcrew member on his/her own volition do the tasks in
Question 74 above?
A-75. Yes, but the flightcrew member’s decision to perform any
task for the certificate holder during a rest period must
be entirely voluntary. This could also include voluntarily
performing computer based training, monthly schedule
bidding, required safety reports, etc.