Ugh, that's a bleak outlook. Days.
Another 50-70 years earlier, someone with locked-in syndrome would likely have benefitted from an awesome treatment called trepanation, in the early 20th century they might as well have enjoyed the benefits of
electrocution electrostimulation in one of its forms (at that time likely alternating-current cranial electrotherapy, two decades later electroconvulsive therapy would be en vogue).
Which, given the state of technology, was not much better than trepanation. Neither treatment precisely increases the subject's lifetime (or does anything beneficial for that matter), so... that's that.
On a more serious note, pressure ulcer is a frequent complication, and a cause of infection and death even today. In the early 20th century, neither was there any understanding of the problem or its causes, nor were there any applicable preventive measures or cures (clinitron bed, vacuum-assisted closure). Antibiotics? Well, come back in three decades. Someone being paralyzed/atonic in an early-20th-century style of bed... I'd expect Bad Things™ happening within days.
Parenteral nutrition with the goal of mid-term to long-term survival (that is, more than a few days) is only possible since the 1960s with Steramin and Lipofundin being among the earliest, and rather insufficient, products available. It really only "works well" since the mid-1980s. In the early 20th century, expect more-or-less isotonic saline infusions so you don't die from dehydration right away, if you're lucky. But surely, not much more.
Surgically-placed feeding tubes have been available since the late 19th century, so there's that possibility. Rates of success (in particular long-term) were, on the other hand side, not so great, as indicated by the word "desastrous" in [Minard G 2006] for... rather obvious reasons. Trans-esophageal feeding tubes have been used for two thousand or so years, but the lack of understanding in nutrient requirements made sustaining a person for more than a few weeks a "challenge". For example, the notion of essential amino acids only became known in the mid-1930s at all.
Then of course, you may have read the stories of Edgar Allan Poe. Although not likely in case vertical eye movement ability is retained, nevertheless possibly, someone suffering from locked-in syndrome might just get buried!