Eukaryotic genomes produce RNAs lacking protein-coding potential, with enigmatic roles. We integrated three approaches to study large intervening noncoding RNA (lincRNA) gene functions. First, we profiled mouse embryonic stem cells and neural precursor cells at single-cell resolution, revealing lincRNAs expressed in specific cell types, cell subpopulations, or cell cycle stages. Second, we assembled a transcriptome-wide atlas of nuclear lincRNA degradation by identifying targets of the exosome cofactor Mtr4. Third, we developed a reversible depletion system to separate the role of a lincRNA gene from that of its RNA. Our approach distinguished lincRNA loci functioning in trans from those modulating local gene expression. Some genes express stable and/or abundant lincRNAs in single cells, but many prematurely terminate transcription and produce lincRNAs rapidly degraded by the nuclear exosome. This suggests that besides RNA-dependent functions, lincRNA loci act as DNA elements or through transcription. Our integrative approach helps distinguish these mechanisms.