Indeed there were some proposals in the past (also in this forum) that this could be an opportunity to "return lost Bitcoins into circulation" -- i.e. set a deadline to transfer coins to a quantum-safe address, and all the coins which aren't transferred, are considered lost and locked to avoid theft. These coins, according to the proposal, could then be added to the miners' rewards from the next halvings on.
This is the theory. However, it would probably lead to a disruption in Bitcoin's price, this means probably a significant downtrend or crash. The reason is that people are already pricing in the "scarcity" generated by the "new supply reduction" after the next halvings, and while the 21 million BTC limit would not be changed, there would be more new Bitcoins on the market in the future. "Lost bitcoins" are currently "priced in" to be lost forever.
Thus, I don't consider this a good idea, and afaik the reaction of the Bitcointalk community to this proposal was universally negative.