Which, that, and who can act as tip-offs about whether a modifier is restrictive or non-restrictive. For instance, a modifier proceeded by that is typically restrictive: “This is the green house that we bought last summer.” Which, meanwhile, typically proceeds non-restrictive modifiers: “The house, which we bought last summer, is green.”
Who, meanwhile, is a little more context dependent. For example, you can have “I need to meet with the one who filed the budget”, which is restrictive, but you can also have “I met with John, who filed the budget”. Often it requires your discretion as a writer to distinguish the two. However, if the modifier is restrictive, then who will usually be interchangeable with that.