For a convergent positive series, we study the properties of the set of all possible subsums. It is well known that the aforementioned set, up to homeomorphism, is either a finite union of closed intervals, Cantor set, or M-Cantorval. The last case is quite complex and understudied. Formally, M-Cantorval is a perfect set on the real line, which is the closure of its interior, and the endpoint of any nontrivial component of this set are accumulation points of trivial components. Our focus lies in identifying the necessary conditions for the set of subsums to be a Cantorval and investigating its structure.