The drop in the penetration of landlines has a clear effect on the ability of pollsters to reach some segments of the population using the standard phone surveys. Namely, younger people (although the problem is obviously not exclusive to that group) not only are less likely to have a landline, they are also more likely to not answer the phone.
I very much like this experiment that the GESOP carried last year on the complementarity of phone and online surveys as a way to handle this problem in Spain. As they state in the presentation of the report:
The test allows us to conclude that the combination of both methodologies (phone and online interviews) in studies of public opinion is feasible. We do not observe significant differences in the results of either technique and the existing ones cannot be attributed to the method of gathering information. In addition, it was possible to reach in a more effective and efficient way different segments of the population under study.
It therefore replicates the basic findings of Ansholabehere and Schaffner (2014).
The most interesting result from my perspective is that, reachability and participation aside, all the differences between the two modes of interview seem linked to the fact that online surveys are usualy self-administered which gives individuals more privacy and a better sense of all the response options that are available to them.