The traditional Gram staining procedure kills the cells during the process. Since the primary purpose of the original Gram stain was to identify and categorize the bacterial cells, the fixed cells color and morphology was most important, so the cells were not required to be living. However, select vital stains (dyes that affect living cells and are not cytotoxic) can be employed for a modern variation on Gram staining, if further characterization of the cells is desired. Fluorescence microscopy (instead of traditional confocal light microscopy) is also an alternative method of analysis, to minimize photobleaching and prevent unnecessary stress for the cells.

References:

1. Mason, D. J., Shanmuganathan, S., Mortimer, F. C., & Gant, V. A. (1998). A fluorescent Gram stain for flow cytometry and epifluorescence microscopy. Applied and environmental microbiology, 64(7), 2681–2685. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC106444/
2. Beveridge, TJ. (2001). Use of the gram stain in microbiology. Biotech Histochem. 76(3), 111-8. https://www.ncbi.nlm.nih.gov/pubmed/11475313