How to parse "this is so they can..."
Ligaments connect bones to each other. This is so they can help stabilize the joints and provide structure to the skeletal frame.
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Parsing one:
"So they can help..." is predicative.
Parsing two:
"So" is predicative and there is a "that" omitted, i.e. "This is so （that）they can help stabilize...". That-clause is a adverbial clause of result.
Which parsing do you think is correct?
Ligaments connect bones to each other. This is [ so (that) they can help stabilize the joints and provide structure to the skeletal frame ].
Your parsing is not quite right. The bracketed element, "so (that) they can help stabilise the joints and provide structure to the skeletal frame" is a PP (preposition phrase) consisting of the preposition "so" as head + the that clause as its complement. The subordinator "that" is optional in this case.
The PP is predicative. It serves as a purpose complement, a subtype of ascriptive predicative complement: it ascribes a purpose to the predicand.
Both are correct in this case.
This is because so can be used to express either purpose or consequence of an action but this may lead to ambiguity. When we are emphasizing the purpose of something, we often use so that to emphasis a purpose but we may choose to omit the that part.
I switched off the lights so that she can get some sleep
I switched off the lights so she can get some sleep
However when we are talking about only the consequence (result) of an action, we must use so only on its own.
It was quite hot, so
thatI opened all the windows