Asreading articles ("As I was reading articles" is okay), I encountered a strange grammar structure. train surfertrainsurfers die each year doing their deadly sport.
sitingsitting on a couch eating popcorn"
The first participle-clause modifies "die"; the second "sitting".
We can use a whole clause - be it tensed or tenseless (your examples) - to modify verbs. The upside of tenseless clauses is that they are more compact, and the downside is that they are often open to more than one interpretation. In your first sentence, for example, the -ing clause can be interpreted as a clause of reason as well as a clause of time.but not clear about the grammar point, why they used ING-formed verb here.