When running a private Ethereum network not requiring gas for transactions, can a contract function transaction fail for some "unpredictable" issue, other than explicit invocation of assert()/require()/revert(), for example dividing by 0 or some other issue with EVM or beyond EVM?
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division by zero
integer overflow/underflow in Solidity 0.8+ (previous versions let the number overflow, 0.8 throws an exception)
accessing out-of-bounds array index
message call (aka internal transaction) to an address that does not implement the called function (might have been selfdestruct or changed implementation behind a proxy)
These I could think of right now. I'm sure there's more examples, generally runtime errors cause by some logical mistake.

Petr Hejda
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Thank you. I suppose in all those cases a transaction would still be created on the blockchain but in failed status. – AndCode Jun 22 '22 at 02:33
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1@AndCode That's correct. – Petr Hejda Jun 22 '22 at 08:07