If two particles are entangled, their quantum states are correlated in such a way that measuring one particle's state provides information about the other particle's state. However, until a measurement is made on either particle, both particles remain in a superposition of possible states, and their individual states are indeterminate.
Now, if you were to destroy one of the entangled particles, such as by performing a measurement that collapses its wavefunction, the entanglement between the two particles would be broken. As a result, the remaining particle would no longer be entangled with anything and would be described by its own independent state.
At this point, without further entanglement or interaction with other particles, the state of the remaining particle would still be indeterminate. Quantum mechanics allows for superposition and indeterminacy to persist until a measurement is made. So destroying one entangled particle does not automatically determine the state of the other.
To determine the state of the remaining particle, you would need to perform a measurement on it independently. The outcome of that measurement would then determine the specific state of that particle, collapsing its wavefunction into a definite state.
It's important to note that the act of measurement itself causes the collapse of the wavefunction and determines the particle's state. This collapse is a fundamental and puzzling aspect of quantum mechanics that remains the subject of ongoing scientific investigation and debate.