Church lady welcome to CAF.
There’s no single answer here. There is canon law and also in the US there’s the Dallas Protocol or Charter, which pertains to sex abuse.other countries may have some parallel.
“Suspended” may mean different things. A priest accused of sex abuse will, nowadays, be removed from active ministry for the investigation. He retains his position as pastor or whatever but does no priestly work.
If the diocesan investigation process deems him to be unsubstantiated, and if the diocesan review board deems him able to return to ministry. he resumes ministry. No referral to Rome.
If the investigation and review process finds he did “something” it gets complicated. If it happened 30 years ago, and if he has gone to an evaluation of current risk, he might be reinstated to some kind of ministry, though this is far less likely than a few years ago. He might simply be held in permanent suspension, with no laicization or referral to Rome.
In this case he is still “attached” to the diocese, may still get financial support. Today it is much more likely he would be referred to Rome for laicization.
Religious order priests are a different process. He might still be referred for laicization (far more likely now than before) yet still remain as a member of the community.
In my diocese the failure to refer for laicization was rightly identified as a sign the diocese didn’t take abuse seriously. But now they seem to go to the other extreme, one-size-fits-all.