This will not be a stellar explanation, but here goes…
Often there is a comma missing before “with” – that is, in qualifying clauses or whatever they’re called.
Example:
“He went to sea with an oar as his sole companion.”
Clearer to my ear/eye:
“He went to sea, with an oar as his sole companion.”
Another, real example:
“It is also unregulated and mostly part of the grey economy with known breaches of worker’s rights.”
No.
“It is also unregulated and mostly part of the grey economy [COMMA] with known breaches of worker’s rights.”
Sometimes the comma-less “with” seems to aim at emphasis, as in:
“This is the total population of the Mediterranean with the Island of Sicily.”
How about?
“This is the total population of the Mediterranean, INCLUDING the Island of Sicily”?
Ask your grammar professors for a better explanation.
In the meantime, be vigilant!