Altering the particle (as far as anyone knows) breaks the entanglement. The person on one end can measure their particle, but that doesn't tell them anything about whether or how the other one was altered.
Once you observe your particle, you've collapsed the wavefunction of the entangled pair. But- crucially- it's not possible to observe the wavefunction itself, so nobody else can tell whether it's collapsed. That is, if I measure my particle, I have no idea whether the particle on the other end will or has already been changed or observed, and I can't know. It just gives me a random value and collapses the state if it hasn't already.
It's only in retrospect that you can detect entanglement; the values you get upon observation of the pairs are correlated once you have both sets of values to compare. But until then you just have a bunch of white noise, and it's not possible (this is the no-communication theorem) to make any sense of that white noise.
Or would it be like where entanglement through time may be possible, the original measurements in both boxes would change instantaneously if the 'later' box was changed so it's, as far as we know, unmeasurable?
Could you create a black box of entangled particles and a code to read them and post it and just hope someone would write to you from the future and you could read it? Sort of like Hawking's time travel party nobody showed up to but for information and just hope something shows up someday. So the code never changes, but the entangled particles in the box can. This could potentially get around the problem of not knowing if the particles were switched in the box. You know the code which doesn't change so you could simply read the box every day and hope that someone from the future had set the particles to a definite state that was readable. I understand that if the particles are observed it doesn't automatically change the particle, but if the particles are observed one way and are continuously observed then they must stay that way, and then the entangled particles must be the opposite of that. From what I understand you're saying it'd be a one and done transmission, but then it wouldn't break the no communication theorem and would be ftl (using a slower than light method, the code which would travel through time at regular speed, to jumpstart the process).