Supplementation vs. Subordination

The Cambridge Grammar of the English Language (Page 1359) has this sentence as an example of supplementation:

(1) Too afraid to venture out, Kim stayed barricaded in the house all week.

Where the adjective phrase Too afraid to venture out is treated as a supplement.

CGEL doesn’t treat the supplementation as a syntactic constituent. This means that the adjective phrase is not a syntactic constituent of the main clause.

Now, I think the above sentence means:

(2) Because she was too afraid to venture out, Kim stayed barricaded in the house all week.

or

(3) Kim stayed barricaded in the house all week because she was too afraid to venture out.

Looking at (3), I think because she was too afraid to venture out is not a supplement but a modifier. If it’s a modifier, it’s a syntactic constituent of the main clause.

Can we say the same thing for (2), or is Because she was too afraid to venture out a supplement in (2)?

If it’s not a supplement but a modifier in (2), how do you justify treating Too afraid to venture out as a supplement in (1) whereas treating Because she was too afraid to venture out as a modifier in (2)?