Such a scenario happens every once in a while and when asked when did the person begin having such a serious condition and/or is bedridden, or was warded in a hospital, the answer is sometimes: "Oh... about 2 weeks ago," or "warded last week," or "quite some time back."
Then when asked, "why did you not ask for the priest to come earlier, so that the person could have his/her confession heard, and then receive the sacrament of anointing and where possible, the Eucharist, some become emotional and blame the priest for being insensitive, or for not being caring or concerned. Some even think that the priest is to be called only when the last rites are to be performed, and calling the priest early would seem like taboo, or "pantang larang" (Malay word for "taboo"), or as if it were a death sentence for the person involved, or something undesirable unless absolutely necessary.
But the reality is this: when something important occurs, would one wait till the last minute then only do something about it? For example, if one has a toothache, one would not wait till the the pain becomes worse or even excruciating, then only go to see a dentist. Likewise, when one discovers that one has got a disease which has not yet reach a critical level, one would not hesitate to seek early treatment to improve one's chances of survival. When we have an exam coming up, we would not wait till the last minute to study and prepare for it. Also, when one discovers that one had left the fire on at the stove or the tap on at home, after coming out of the house and driven a short distance away, one would quickly drive back to the house to switch off the fire or the tap to prevent disaster from happening, or ending up with a hefty water bill.
If we can take precautions for such situations and many more, then surely we ought to take precautions and inform the priest early, so that the priest could provide the necessary pastoral care to the person while there is time and opportunity to do so. When we procrastinate and delay in seeking the priest, are we possibly jeopardising the person's spiritual well-being and putting the Lord to the test? Thus, let us not wait till the last minute, since by then, it may be too late.