My Rotel HT system does .
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I have an old Harman Kardon amp from the mid 90s that has that option.
As for subs, most powered subs offer this option.
A while back I bought an amp on ebay (can't remember the brand) that was listed as "dead" for parts only. When it arrived I noticed it had an auto on switch. I turned the switch off and the amp worked great. After some research I adjusted the auto on trigger and that worked great also.
The (low-end) Sony subwoofer I use for home theater does this and it's a real bother (relay is very noisy).
Frequently clicks-off when no LF present in program.
Another function I've seen is auto off-on (Pretty sure my ARC VT-100 had this). A control cable is used to turn amp on-off depending on the state of the pre-amp.