The current ecosystem of single-cell RNA-seq platforms is rapidly expanding, but robust solutions for single-cell and single-molecule full-length RNA sequencing are virtually absent. A high-throughput solution that covers all aspects is necessary to study the complex life of mRNA on the single-cell level. The Nanopore platform offers long read sequencing and can be integrated with the popular single-cell sequencing method on the 10× Chromium platform. However, the high error-rate of Nanopore reads poses a challenge in downstream processing (e.g., for cell barcode assignment). We propose a solution to this particular problem by using a hybrid sequencing approach on Nanopore and Illumina platforms. Our software ScNapBar enables cell barcode assignment with high accuracy, especially if sequencing saturation is low. ScNapBar uses unique molecular identifier (UMI) or Naïve Bayes probabilistic approaches in the barcode assignment, depending on the available Illumina sequencing depth. We have benchmarked the two approaches on simulated and real Nanopore data sets. We further applied ScNapBar to pools of cells with an active or a silenced nonsense-mediated RNA decay pathway. Our Nanopore read assignment distinguishes the respective cell populations and reveals characteristic nonsense-mediated mRNA decay events depending on cell status.