Steps:
1. Connect to PC with Steam Link and enter Big Picture Mode
2. Steam Menu -> Power -> Change Account
3. Do you wish to continue? -> Confirm

Expected behavior:
Same as when using Big Picture Mode locally - I am shown a list of other Steam accounts that have been logged in and can log in as a different one.

Actual behavior:
The stream is killed when Steam logs out of the current account. The only way to change the account - or even continue as the previous account - is to access the machine locally or through some other remote access software.

Proposed solution:
Move Steam Link/Remote Play process into a system service that continues to run even if the Steam client frontend needs to close (e.g. during Change Account procedure).