This can be very confusing.
Start with a simple situation, when
time = 0 is both the time of study entry and the time of starting some therapy, for example in a cancer outcome study in which you want to evaluate time to death after therapy starts. If Participant A both enters the study and starts therapy at
time = 0, and is still alive at
time = 2 years, then you know that the time between starting therapy and death will be at least 2 years for Participant A. That's standard right-censoring at 2 years.
Now say that Participant B enters your study after having started treatment at some prior unknown time. You don't know exactly when treatment began, so you call
time = 0 for Participant B the time of study entry. If Participant B dies at
time = 2 years, you know that the time between starting therapy and death was at least 2 years. That's logically the same as for Participant A: in both cases, you have a lower limit on the time between starting therapy and death. That's right censoring on the survival time of interest in both cases.
Potential confusion with Participant B can come from losing the more typical association of lack of an event with right censoring, which you do have with Participant A. With Participant B you observe an event but you don't know the actual elapsed time from starting therapy to death, so you have to treat that event time (starting from your
time = 0 at study entry) as a right-censored observation.