How to support a boyfriend when his father has passed away?

Okay so I have been with my boyfriend for about 10 months. Lately my boyfriend has mentioned he has not been feeling so well. He claims he is dehydrated, weak, dizzy and etc; He hasn’t felt well before in our relationship and he feels distant.. but I just realized tomorrow will an year since his dad passing and I am wondering maybe that’s why he is feeling this way. I never brought up the date of his dads passing because I felt awkward and didn’t know how to bring it up... as I never dealt with a family or someone close passing away. I found the date of death on the online obituary as we searched his name on google before (his dad shares the same name as him)
lately he has seemed withdrawn and not texting as much.. he has always been not the greatest texter but he informed me yesterday that if he doesn’t text he is going to be wrapped up in his blanket because he doesn’t feel good.. but I haven’t heard from so far today.. so I don't know if he is really not feeling well because he has been overworked and tired or it’s his dad passing too making him feel under the weather..

should I bring up his dad passing and let him know I’m here for him or just give him space.. ?
I just want to be supportive.. but I don’t want to come over the wrong way and be “annoying”...
How to support a boyfriend when his father has passed away?
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