Praise be to Allah.
Firstly: It is permissible to feed dead meat to animals that are not eaten, such as dogs and cats, and that includes pork, which is dead meat in all cases, whether it is slaughtered or it died without being slaughtered.
Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo’ (4/336): It is permissible to feed dead meat to dogs and birds, and to feed impure things to animals. End quote.
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: It is permissible to put out fires with wine, and to feed dead meat to falcons and hawks, and to clothe animals with impure cloths, and to use impure oils in lamps, according to the more well known of the two scholarly opinions, which is also the better known view of Ahmad. That is because using impure things is a way of using them up without causing harm. End quote from al-Fataawa al-Kubra (1/433).
It is not permissible to sell pork, whether on its own or mixed with other things, because of the report narrated by al-Bukhaari (2236) and Muslim (1581) from Jaabir ibn ‘Abd-Allaah (may Allaah be pleased with him), that he heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say during the year of the conquest when he was in Makkah: “Allaah and His Messenger have forbidden the sale of alcohol, dead meat, pork and idols.” Al-Nawawi (may Allaah have mercy on him) said: It is permissible to feed dead meat to carnivores but it is not permissible to sell it. End quote from al-Majmoo’ (9/285).
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about cans of cat food that contain pork – is it permissible to buy them and feed them to cats?
He replied: If that is by buying the cans then it is not permissible, because it is not permissible to pay for pork and buy it. But if he finds it thrown away and feeds it to his cat, there is nothing wrong with that. And Allaah knows best.
See the answer to question no. 5231.
Based on that, it is not permissible to work in a food factory where pork or other kinds of dead meat are used, because that is helping in sin and haraam things, as it is manufactured with the aim of selling it, which is haraam as stated above. Allaah says (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment”
And Allaah knows best.