In the Advanced Race Guide, the rules for creating custom races presents an interesting question. The Half-Construct subtype can be applied to the Outsider (Native) creature type. However, Native Outsiders can be raised, unlike standard Outsiders, but Half-Constructs cannot. Which would take precedence and why?
Half-construct takes precedence.
Being a native outsider means you are treated normally (like a human, elf, or pretty much anything else) when it comes to resurrections, instead of the special outsider limitations. A half-construct human could not be raised, so the same should apply to a half-construct native outsider.
Basically, being a native outsider doesn't grant you the benefit that you can be raised normally. Most creatures have that - it is the default assumption unless noted. Instead, you just don't gain the outsiders drawback.