What happens if you perform restriction digestion with an enzyme that does not have star activity but leave them for more than two days? will the overhangs be removed or chewed off? will Ligation work after purifying this product?
No worries. All enzymes have activity window in which they are active ( How long it varies and it depends on the type of enzyme ). Like above I also think you are good to go. Usually, I use nuclease free water whenever I am setting up my restriction digest.
I don't know of any manufacturer who will guarantee that their enzymes are free of star or unspecific nuclease activities for an unlimited period of time. Nor do I see the benefit of performing restriction digests for over two days. Generally, it is advisable to stick to the recommendations of the manufacturers. If there is a problem it is likely due to some impurity in the DNA substrate that inhibits the reaction and it would be better to improve that parameter rather than increasing incubation time beyond reasonable (overnight).
If you are checking only digestion No problem with your digested product until you have used less unit of enzyme. If you are proceeding with downstream experiment like ligation and for cloning it is advisable to digest maximum of 4 hours or over night with less unit of enzymes.