I'd suggest considering this within the context of your food defence plan - whilst the access gained to product/vehicles/property certainly isn't malicious, it does relate to security and could certainly have implications for food safety.
Certainly you should inform the police or an appropriate authority (otherwise you are in effect an accessory to any crime that may have been committed), and potentially obtain medical assistance.
And treating those you've found with civility seems to be the sensible thing to do as well, if they arrive at the delivery point. Exactly which bits of the site you can give them access to will depend on the layout, so you'd need to consider what it might mean in your situation. My inclination would be to make sure everyone was warm, had a cup of tea (I'm British ), food etc., but equally it probably isn't sensible to compromise any of the actual production activities to achieve this. Nonetheless I think it requires broader discussion within a business to decide on such things - as an individual I'd happily scrap a day's production to prioritise care for fellow humans, but business agendas don't always align with personal ones...
It's also worth bearing in mind that sticking around may not be their intent, as they may wish to avoid the authorities in the country in which they arrive.
In terms of the implications for the product, you may need to look at the risk based on the nature of the product and how it is transported. Is it genuinely secure and sealed, e.g. metal drums with numbered metal security seals such that you can really prove nothing has happened to it?
Quarantine should be a default initial response, to allow proper assessment in terms of potential risk, and I'd take a very risk-averse position on this; anything that can't be proven to be completely uncompromised should be scrapped IMO. Might also be worth discussing with your insurers - it's a bit easier getting clarity on it in advance, than it is in a "live" situation. Similarly it also helps if you have clear definition
I have had some experience of this, although not as far as arriving at site. During the period when lots of migrants were trying to enter the UK from Calais we had several incidents of people trying to get into tankers. I think it's a mark of the level of desperation these people are feeling when they are willing to consider climbing into a closed tank of 25000L of cold liquid to attempt to make the journey to another country...
Thankfully no-one actually managed it, as I think it would be very likely to result in death by drowning and/or hypothermia.
Our default approach was that every tanker on which a seal had been broken was rejected.