For example, if Johnny Manziel is under contract with Cleveland for the 2016 season, he will likely get put on waivers and a suspension from the NFL.
Will he get credit for serving a suspension (e.g. 4 games) while he is on waivers?
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NFL suspensions, when for a particular number of games, do take place even when as a free agent.
For example, Laron Landry was suspended for the first 10 games of the 2015 season for PED use; after week 10 he was reinstated despite not being on a team's roster for that period of time. (He was subsequently suspended again, of course... some people never learn.)
So, if Manziel is suspended a specific number of games (say, 6) for his domestic violence incident, he would serve those regardless of whether he was on a team's roster or not.
However, in some cases the Commissioner will suspend a player "indefinitely" (for example, another popular Browns player, Josh Gordon, is suspended indefinitely, but can apply for reinstatement after a year). The commissioner likely has more leeway in those cases.