If you do not say anything, the only danger is that the caller knows that the number is live. But that does not seem to be a big risk as they seem to think it's live.
Answer but say nothing except "who is it please?" then mute the phone to help you resist the temptation to say anything. The crooks on the phone are experts playing on people's emotions to get them to engage. The trick for you is to say nothing except to ask questions. Do not give any information but turn each of their questions into question. It may sound childish and rude, but it is effective.
Legitimate businesses have many legitimate reasons to call you while hiding their number. If you discover that it is legitimate, you should be able to go to the official website to get a number on which you can call back. Aim to do that.
If it is not legitimate, call your telephone company to have the calls blocked.