I love how one little verb can carry so many vibes — 'succumb' is one of those. When I use it, I usually think of two main flavors: giving in and being overwhelmed. For the "give in" sense, the common synonyms I reach for are 'give in', 'yield', 'submit', 'surrender', 'capitulate', 'relent', 'cave in', and 'acquiesce'. Those fit nicely when someone yields to pressure, temptation, or persuasion. In a spicy chat or a dramatic scene in a novel, 'cave in' or 'give in' feels casual and vivid, while 'capitulate' or 'acquiesce' sounds more formal and a touch colder.
For the "be overcome" or physical/medical sense — like "succumbed to his injuries" — I switch to 'be overcome', 'fall victim to', 'yield to', 'die from', 'pass away from' (gentler), or even 'perish'. I try to match tone: 'pass away from' or 'die from' for compassionate writing, 'perish' for older or epic prose, and 'fall victim to' when you're emphasizing external forces. I often mix examples in my head from games or books — someone who 'caves in to temptation' in a RPG, or a tragic NPC who 'falls victim to an infection' — it helps me pick the right synonym for the mood.