When a question is posted on one site and then migrated to another, if it ends up closed for any reason, it ends up locked on the new site. That is, it can't be voted on or edited. A diamond moderator on the site can unlock it, though.
It's fine to lock a question that is closed as off-topic, since that means it falls outside of the scope of the site. It's probably going to be very difficult to make something that is off-topic become off-topic, unless you change the question to something radically different. If it already has answers, it's probably better to just start a new question.
However, when a question is one of these other reasons (primarily opinion-based, too broad, or unclear), it's possible to clarify the question. Either regular users can come along and edit it or engage the asker in comments to help clarify. The target site may be in a better position to make the changes ask the clarifying questions that will make it not primarily opinion-based, too broad, or unclear because they have the expertise in the subject matter (which is why a question would be migrated anyway).
There's also a philosophy of closing fast. I'm not sure how many sites subscribe to this theory - Software Engineering does, and I've said that it has worked wonders. We've had more than a handful of questions edited into shape after closing quickly and engaging the author in comments or chat, and these often turned out to be good questions. Closing fast prevented low quality answers that are usually drawn to low quality questions making this possible.
As much as I disagree with migration existing, if it's going to exist, it should be useful to help get good answers out there. When an on-topic, but borderline question is migrated from a site with limited expertise to one with high expertise in the topic, the high expertise site should be able to follow a close fast policy (if it is their norm - and I think it should be a standard practice, but that's another discussion) yet still be able to engage and fix.
I think this is important because if the author can't fix their question, I think they are likely be become disengaged and ignore it. This makes a breakdown in how a community works when they fast-close a question that they hope to salvage by working with the original author or among themselves.