Captain reported they learned the runway at FSD was closed only after they overheard airport maintenance advise a departing aircraft they had departed a closed runway.

Narrative

I witnessed an occurrence the other night at FSD [airport] which negatively affected another pilot and should be of concern to us. I also feel the FAA should be aware.At about XA:57 as my First Officer and I (Captain) were inbound to FSD about ten miles out and planning Rwy 3; we heard another aircraft -- having just taken off -- report turning to the south. Moment's later airport maintenance radioed to tell the other aircraft he had just taken off on a closed runway; as Rwy 3 was closed.My flight had been called out at XA:00; and I told my copilot that I hadn't seen any NOTAM for runway closure; so I quickly pulled up online ADS-B data and saw a NOTAM effective at XA:49 til XB:30 for Rwy 3 closed.At no time did I hear airport maintenance announce on the radio that Rwy 3 was closed; and I did not hear airport maintenance advise the other aircraft of the closure after any of his radio calls. We had just canceled IFR with MSP Center 25 miles out and the controller hadn't mentioned any runway closures; so this NOTAM was very recently filed.This is concerning. A last minute NOTAM and no monitoring on the radio and no communication to an airplane taxiing to and departing from a very recently closed runway puts us all at risk of a violation; and filming a perceived infraction in lieu of a radio communication shows a deliberate attempt at entrapment.There needs to be a change in communication procedures. Airport maintenance needs to give more notice when filing NOTAMs and needs to be cognizant of aircraft that may not have had an opportunity to be informed. Education on how a flight's preflight planning and a Go decision" is conducted might be helpful.For now; I will alert my fellow pilots that if we operate at FSD while the tower is closed and maintenance is out and about; to query them about runway closures and airport maintenance personnel's location."