If some nodes change their way of accepting blocks, then those nodes will be dropped from the network. The Bitcoin miners and Bitcoin nodes will continue running without the modified nodes and ASIC will continue to work as they always have.
The question is: Who will be dropped from the network, miners or majority of nodes?
Both. The network splits into "original bitcoin" and "new protocol trying to call itself bitcoin" if there isn't 100% consensus.
Suppose that 7 largest mining pools are running 0.11, while 5000 nodes (including exchanges) have upgraded to 0.13, which is a softfork and backward compatible, then which one is the real bitcoin?
Fully backward compatible? Then they can both be "the real bitcoin". In order to be compatible, they can't break any of the current consensus rules, so it won't matter.
The difference is, in 0.13 you can spend Satoshi's one million coin with a newly defined key, because the block structure is different. But in 0.11 you can not.
Then it isn't a soft fork, and it isn't backward compatible. The network splits into "original bitcoin" and "new protocol trying to call itself bitcoin". The only way that the new protocol can "win" is to convince nearly everyone (exchanges, merchants, consumers, investors, etc) to use their new "stealCoin" protocol instead of the secure "Bitcoin" protocol.
So the decision falls on these miners: They either stay at 0.11 and protect Satoshi's coins which no one cares, or they join majority of the nodes and share Satoshi's coins 
Actually the decision falls on everyone. If everyone refuses to use the insecure "stealCoin" altcoin, then it will fail. If everyone thinks that allowing theft is the better way to go, and they don't care if it will be used to steal form them someday, then your "stealCoin" altcoin will succeed and Bitcoin will be a failed experiment.