:up: He (some adult - perhaps he'd 'nodded off' in the armchair in his study) slept on [='continued sleeping]. 'One small hand' [a child's] 'closed on the letter' [='began to take a grip on it
{presumably with a view to taking it stealthily* from the sleeping man}].
Your trouble is no doubt due to the fact that both 'slept on' and 'closed on' have more than one meaning. In some possible combination of these meanings, maybe one 'completes' the other.;-)
b
PS* If this word is new to you, you'd be right in thinking that it was related to 'steal', but WRONG if you thought that they share a vowel: /sti:l/ but /stelθɪli:/ - sorry,
- that's just the way the language is!