I understand that miners are never gonna stop mining given the transaction fee reward for each block. But just in case of an event when nobody is able/willing to mine the next block in the blockchain, what happens to the new transactions, how are they supposed to get published? And also, how is it going to effect the blockchain consensus?
They don't. The blockchain is by definition a chain of mined blocks. If nobody mines the next block, then the blockchain cannot grow, and no further transactions can be included in it. Transactions will cease to be confirmed until somebody does mine another block.
Transactions can still be relayed over the peer-to-peer network, and nodes will verify their signatures and store them in their mempools, but there will be no real protection against double spending. Someone might create two or more transactions which conflict; some nodes may store one and others may store the other. No consensus will necessarily arise as to which one should be accepted as the "right" one.
If this state of affairs becomes permanent then the currency is effectively dead.