Custom unique constraint, only enforced if one column has a specific value
In other words, you want values in the column subset to be unique among rows where the column type is 'true'.
A partial unique index will do that:
CREATE UNIQUE INDEX tbl_some_name_idx ON tbl (subset) WHERE type = 'true';

Data type does matter. If the column type is boolean (likely should be), you can simplify:
CREATE UNIQUE INDEX tbl_some_name_idx ON tbl (subset) WHERE type;

This way you can even make combinations with NULL unique, which is not possible otherwise. See:

PostgreSQL multi-column unique constraint and NULL values