Participial clause?

Solution 1:

McCawley doesn't say much about it, as far as I can see, but it appears to be a variety of the complex of serial verb constructions around motion verbs and their inchoatives and causatives, like the various serial verb constructions mentioned in this freshman grammar exam question (#4, restricted to come and go):

• Bill went and dug some clams. (go and + V)
• He asked us to come eat the clams. (come + V)
• He said “Come and get it!” (come and + V)
• We’re going to go eat them. (go + V)
• We'll go swimming afterwards. (go + V-ing)
• We'll come strolling in late tonight. (come + V-ing)

But there are lots more verbs that cause motion, and motion has a number of verb-like properties, so this construction complex gets much broader in scope. E.g,

Harry swung at it with the bat
to stop it from breaking his nose,
and

• went muttering curses out the door
• came lurching out the door
• brought her shuddering back to consciousness
• plucked it screaming out of the air
• sent it zigzagging away into the air
• tossed it spinning down the stairs
• dropped it unmoving into the cauldron

There are a number of possibilities here:
the initial verb part of the serial verb may be

• an intransitive motion verb (go, come)
• a transitive causative/inchoative of a motion verb (respectively: take, bring)
• a transitive verb that entails some kind of induced motion (pluck, send, toss, drop, etc.)

while the gerund part normally describes some property of

• the motion induced by the verb (lurching, zigzagging, spinning), or
• the object or person caused to move (muttering, shuddering, screaming, unmoving)

In either case, it is the moving object that functions as subject of the gerund constituent and displays the property; one may give it several different kinds of PS, but I'd treat these more or less the same way I treat phrasal verbs, as a discontinuous construction with two parts that share the semantic load, subject to easy idiomatization and extension to many metaphors.

Solution 2:

I think part of your difficulty is that you're trying to make your analysis 'worry' about things that traditional grammar worried about but which aren't really relevant to a modern analysis. Remember that in a modern analysis:

• you are not constrained to the traditional assumption that every grammatical feature must be overtly present (in other words, you can have things like null subjects and tree nodes that are theoretically assumed to be present but not actually filled by any word/phonetic content);
• constituents representing traditional notions such as 'clauses' can actually be a hierarchical structure, with different levels of the hierarchy present or absent;
• there is no obligation to define one single exclusive entity that another entity 'modifies': several nodes can be co-indexed;
• there is no obligation to shoehorn every single word into one of the traditional categories such as 'adjective': what matters is what node a particular item is attached to, and what is that node's surrounding hierarchy.

In other words, in a modern analysis we could say that what we call a 'normal' clause or sentence is some particular tree hierarchy, e.g. a Verb Phrase inside an Aspect Phrase inside a Tense Phrase (among other levels of hierarchy), and that the what we see as a 'participial' clause is a variant of this structure where the Tense Phrase (among others) is absent. There's no consensus as far as I'm aware on any exact structure, but whatever analysis you choose would need to take into account the fact that there clearly appears to be a VP (since the clause can contain an adverb and complement), and there needs to be some node to account for the presence of the -ing inflection.