51% of miners can soft fork and increase the hard limit on # of bitcoins.
Nah, that would be a hard fork.
Hard and soft forks have to do with forward/backward compatibility.
Yes. If blocks according to the new protocol are all valid according to the old protocol, it is a soft fork. But if you make bigger blocks, they are not compatible with the old protocol. So increasing the block size is a hard fork. Because the old protocol doesn't validate big blocks.
Regardless of the mechanism of the fork, it does not necessarily follow that there will be 2 blockchains in the future, if that is what you mean. As long as consensus is reached, there could be one bitcoin blockchain with an inflationary supply beyond 21 million.
The options are more complicated than that. But a SOFT FORK never splits the bloc chain. There is no mechanism with a soft fork only, to have two chains.
If a soft fork is applied by 51% of the hash power, the other 49% of miners have no choice but to join, or to get their blocs orphaned all the time, because *their* (old) protocol ACCEPTS the new blocs as valid, so they have to build upon their longest chain. If they don't, they build a shorter chain (less hash power) and they always get orphaned.
So with a soft fork: no danger for a chain split, and majority of miners IMPOSES its will on everybody.
With a hard fork, that is not true any more. Because the new blocs are not compatible with the old protocol, the old protocol can continue working, even with a minority of hash rate, because the new guys (even majority) seem to make invalid blocs, on which old miners will not build. So you have the old minority chain surviving, and the new majority chain making a different chain.
If the hard fork is bilateral, that means: old blocs are not valid for the new protocol, and vice versa, the split can occur at any ratio between hash rates of miners: the new chain can fork of with minority or majority hash rate ; the old chain can continue to exist.
What will happen, if there are two chains (hard fork only) is that USERS will vote in the market with their money, determine the market caps of both chains, and miners will adapt to highest profitability, which means, they will in the end, split according to market cap (if not, it has an advantage to change camps).