Honestly I don't like this. If the user takes a little bit longer to respond to the warning (eg. examining the threat, making a decision or simply distracted), all their files could be lost in the meantime.
This isn't the case at all! When Emsisoft Anti-Malware displays the alert for the user to respond to, the process being alerted about for the behavior which triggered the alert becomes suspended. This means that all the threads within the target process become suspended, which essentially means they are "frozen"; since all the threads are "suspended", it means they cannot execute any code until they are once again resumed.
A process is pretty much a container, the actual container (the process) doesn't execute the code for the program, but the threads within the process are responsible for executing the program's code... The same way that the heart is responsible for pumping the blood around our body but the body itself is a container for our internal organs, or how our brain allows us to function by sending signals to our muscles but the head is the protector for the brain.
Therefore, when Emsisoft Anti-Malware alert's are triggered, you can take all the time in the world to read the alert properly to understand what's going on and then respond to it.
Edit: This should be the case at least, just read what
@Evjl's Rain said above... Hmm.... I'll do some testing to double check if they changed anything since I last tested?