How to block someone's number but still see if they've tried to contact me?

I'm receiving calls/texts from people who I've recently cut ties with (long history of abuse) and I find it disruptive to be enjoying my day and all of a sudden receive a text from them. I have considered blocking their numbers, but I don't want them to send me a text and me not know about it (e.g. Legal reasons). Basically, I would like to not be notified when they text me, but have the option of going and checking to see if they have (could I unblock their numbers and would missed calls/texts come in?).

It's not very frequent, but for example they might try to contact me on my birthday and I'd rather just not have to deal with that then. I use an iphone and so do all they.

It sounds like it's probably not possible but any insight would be greatly appreciated.

If you have a smart phone look at "blocking" apps, all the apps work a little differently.