Hi, if the bump became very large overnight or in a couple of days, then it is likely not cancer.
"Can fn biopsy give wrong results?"
Yes, because the needle might miss the bad spots. But since 4cm is *very* large, if it were cancer then probably everywhere in the node would be bad spots. So having a negative result in his needle biopsy is probably accurate.
"Can cancerous lymph nodes shrink and again goes bigger?"
Only a little bit smaller, since that would be from swelling/inflammation "waxing and waning". That's not actual reduction of a tumor.
"What should i do??"
The only sure way to know is with an excisional biopsy, where the whole node is removed and analyzed. Since that is a surgery, there is risk in that from anasthesia, infection etc.
You can ask for an ultrasound that would look for the inside of the node being normal, especially having the part called the 'fatty hilum'.
Overall, there isn't any reason to think that the doctors are neglectful here.
Is the bump long and thin or is it round? That's important to know.
So if it's not cancer, then what is it? Probably some infection or immune reaction, and then the forming of what's called 'granuloma' which doesn't go down as you'd normally expect. There would be scar tissue formed inside the node - and even some calcium deposits which make it very hard.
You want to be very aware if it keeps growing. Also he should regularly check neck, underarms and groin for any more bumps. (But pressing a lot on the neck bump could irritate it and make it swell.)
Good luck, to him and to you.