Skeletal muscles in clam
Older papers initially presumed that it was part of a mechanism called "catch" in invertebrates like molluscs which is a "sustained contraction."  However, paramyosin was also found in insects.  There is a very detailed review on invertebrate muscle from 2008 that you should read through (or, you know, search through) points out that recent evidence has shown that paramyosin is not involved in catch; that review also has this to say on the subject (emphasis added):


  Furthermore, paramyosin’s presence in almost every invertebrate muscle (including those with relatively small thick filaments) suggests that paramyosin should not be considered a ‘special’ molecule whose presence needs explanation. Paramyosin is instead an everyday constituent of invertebrate muscles, similar, for instance, to the giant sarcomere associated proteins (see Hooper and Thuma, 2005). Indeed, a more salient question might be why vertebrates do not have paramyosin.