We often omit relative pronouns in restrictive clauses. E.g. "I am flying to a place I love" instead of "I am flying to a place that I love."
It seems ok to omit the which/who in the following. But what are rules for omitting relative pronouns for non-restrictive clauses?
The treatment, which was covered by insurance, lasted days.
The treatment, covered by insurance, lasted days.
John, who was buried in debt, sold his house.
John, buried in debt, sold his house.
"John, who married Susan, sold his house."
and"John, having married Susan, sold his house."
The latter implies that the marriage led to the sale of the house, whereas the former is ambiguous in this regard.