1. i think the OP is assuming that altcoins can replace bitcoin.
a. altcoins dont have the same genesis block
b. all the headers from the genesis block to the newest/current block are unique to bitcoin
c. for an altcoin to even try appearing like bitcoin someone will need to have a copy of the 6 years of tx history and more than 50% hash power of bitcoin
in short litecoin nxt, or even lickyourasscosyoulikit coin can never replace bitcoin
2. if the OP is not talking about altcoins replacing bitcoins blockchain data.
what you are talking about is forks due to a 51%. this topic has been covered maybe 100 times before.
but in short.
even if a miner had 51% mining hashpower. each users bitcoin-core node has a set of rules and if any manipulated blocks that show funds miraculously appearing out of no-where. the user nodes would reject it.
the only possibility would be for a nasty miner to try undoing transactions that happened before, which requires them to backtrack and undo the previous block, solve it and then solve the current block and then solve the next block to get ahead.
this in short means they have to try solving 3 blocks in the time it takes over miners to solve 1 block.
and this my friend is why exchanges only trust transactions that have more than 1 confirmation.
the chances of someone solving 3 blocks is so improbable that it is not worth worrying about, but the safeguard of only accepting payment after 3-6 confirmation (where it requires a nasty miner to solve 5-8 blocks) to mess with. is something unthinkable.
i personally am happy accepting non-confirm transactions or atleast 1 confirm if the value is high. all because the odds of a miner messing with it is too huge to put into numbers.
if you wish to learn more rather than being spoon fed the answers, please research:
51% attacks
confirmations
3. if the OP is talking about bitcoins 'value' continuing to exist. well thats a human decision people make about what they value.
either way the bitcoin blockchain will continue on as long as someone atleast continues to mine it.
I don't make extra assumptions. I'm asking about assumptions required for Bitcoin existence. Regarding the fork it means that
We assume that it's possible to distinguish branches
OR
Fork doesn't happen
At least one of these assumptions is required IMO, but I'm not sure.