This is one reason I think there's a relatively low level of Danish proficiency in adult immigrants: it is virtually impossible to burn your ships in that manner, because ~all Danes speak fluent English, and generally prefer to speak English to foreigners vs. attempt to understand poor Danish. If someone explicitly asks to keep the conversation in Danish, then people will typically oblige and attempt to understand the learner's Danish, but as soon as the person goes to a restaurant or even a government office, it'll be immediately English again unless they ask each time this happens (and even then the person may just honestly not understand them, because Danes are not good at understanding mispronounced Danish).

Two additional factors: 1) Language aptitude is a continuous range, not discrete and 2) unused/unpracticed skills can atrophy. This is particularly evident in very young immigrants who exhibit "receptive" skill in their mother tongue even though they may have had fluency in earlier years. Immerse them in the native language, and they'll often pick up much much faster.

Do you have any cites for this?

I suspected it might be true, and tried actually putting together a paper on this for a class in the early 90's, but pretty much ran into a dead end looking for literature to review at the time.

On a more anecdotal level, I had a funny experience when I went to Japan -- I was somewhat passable in French before I went, and after about half a year of being in Japan (before I had really become fluent in Japanese) I tried speaking some simple French with a French teacher. It was impossible -- every sentence started in French, and ended in Japanese :) After I got better at Japanese, my French started coming back too -- but I'm still hoping to spend a month or two in France to really get it up to a usable level. Interestingly, I didn't have any problems with my English while there -- probably because I was already fluent in English (my mother tongue is Norwegian).