A majority of users would have to upgrade the software for the cap to be changed. Even if 99% of mining power moved to the new cap, the old software would not be compatible with the new fork. It would split the network in two, since users of the old version would see a block that includes a subsidy larger than what is allowed, thus considered an invalid block.
So what would the economic impact be of this sort of split? Imagine a 49/51 split for a protocol change, many of the 49% may suddenly dump and sell off their BTC. Or maybe this sort of thing is just as common in fiat currency like the Cyprus banks changing the rules?