Some opponents of open borders adopt “twofers” — they hedge their arguments against different empirical possibilities by arguing that both of the empirical possibilities are bad. This puts them in the enviable position of making claims that appear to not be falsifiable by the empirical evidence. Some examples are below.

• Work and welfare: Some opponents of immigration argue that immigrants either do work (resulting in suppression of wages of natives) or go on welfare (resulting in problems of abuse/overuse of the welfare state). Some opponents of immigration go further and argue that both happen simultaneously (for instance, they work, but make use of free public schools and hospital emergency services). Bryan Caplan considers this in his blog post Opposition to Immigration: Get Your Story Straight.
• Legal and illegal: Some opponents of immigration argue that illegal immigration is bad because it undermines the rule of law, while legal immigration is bad because legal immigrants become eligible for various welfare state benefits and legal protections.
• High and low skill (see also high versus low skill): Some opponents of immigration argue that low-skilled immigration is bad because of the harms to immigrant-receiving countries, whereas high-skilled immigration is bad because of the harms to immigrant-sending countries. An argument along these lines is offered by Allan Wall in the article Memo from Mexico for VDARE.com:
  

  I’ve always been curious about how stringent a process is used to select foreign nurses.

  If U.S. hospitals are getting the best-qualified foreign nurses, then we are taking these fine workers away from Third World countries, where they are needed.

  If the answer is no, we’re endangering our own patients.

  It’s likely that both scenarios are true, in different cases.