Praise be to Allah.
Beef that has been killed before being slaughtered (i.e., before its neck is cut in the halaal method) is considered to be maytah (“dead meat”) and it is not permissible to eat it, because Allaah says (interpretation of the meaning):
“He has forbidden you only Al Maitah (meat of a dead animal), blood, the flesh of swine, and any animal which is slaughtered as a sacrifice for others than Allaah (or has been slaughtered for idols or on which Allaah’s Name has not been mentioned while slaughtering). But if one is forced by necessity, without wilful disobedience, and not transgressing, then, Allaah is Oft Forgiving, Most Merciful
With regard to what you mention about some Muslims eat meating that has been killed before being slaughtered, it may be that they are sure that the meat that they are eating has been slaughtered according to sharee’ah, or it may be that they are ignorant of the rulings on this kind of meat, or they may have asked (scholars) who told them that this meat is halaal.
Whatever the case, you have to avoid eating these meats, and if anyone asks you to eat it, you should refuse to do so, and explain why you are refusing – so that they will follow that or at least excuse you for not eating it.
With regard to what you mention about some people saying that it is permissible to eat this meat because they are the People of the Book, the answer is that it is permissible to eat meat that has been slaughtered by the People of the Book, but this meat that you describe is not meat that has been slaughtered by them; rather it is dead meat, and it is not permissible to eat dead meat even if it was killed by a Muslim.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said:
“Allaah says (interpretation of the meaning):
‘Made lawful to you this day are At Tayyibaat [all kinds of Halaal (lawful) foods, which Allaah has made lawful (meat of slaughtered eatable animals, milk products, fats, vegetables and fruits)]. The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them’
This aayah makes it clear to us that the food of the People of the Book – i.e., the Jews and Christians – is permissible for us, but if we know that they have slaughtered a permissible animal in a manner other than that prescribed in sharee’ah, such as killing it by strangulation, electric shock, hitting it on the head, etc., then it is meat “which has been killed by strangling, or by a violent blow” (cf. al-Maa'idah 5:3), so it is haraam, just as meat which has been killed by strangling, or by a violent blow by a Muslim is also forbidden to us. But if we do not know what is the case, then the meat slaughtered by them is halaal for us, in accordance with the aayah.”
(Majallat al-Jaami’ah al-Islamiyyah, no. 3, p. 156
In conclusion, we hope that you will spread the fatwa of Shaykh ‘Abd al-‘Azeez ibn Baaz to the Muslims whom you know, as much as you can. And Allaah knows best.