Following a meeting with Council of Europe Commissioner for Human Rights, Nils Muižnieks, LGBT Denmark submitted a number of concerns. The meeting was in preparation to his country report on Denmark. See the submission here: Commissioner_DK_meeting_LGBT
Among other things LGBT Denmark brought to the commissioners attention a case, where an asylum seeker was rejected but could not be returned to his home country and has been sitting i Denmark in a limbo for 15 years.
In his country report, the commissioner spoke out against the situation:
Measures should urgently be taken to put an end to the “legal limbo” of rejected asylum-seekers whose deportation order cannot be implemented. Stays of indefinite duration in asylum centres cannot be considered as a viable option and the willingness of authorities to incite voluntary return should never result in arrangements that impinge on the human rights of the persons concerned and the members of their families. (p. 2 and sec. 56)
See the country report her: CommDH(2014)4_EN