I'm on the team at Sapling Intelligence, a deep-learning AI Writing Assistant. A lot of privacy and security conscious folks don't like the idea of a keylogger, so we have self-hosted/on-premise/cloud-premise options for businesses. We have a list of available offerings here:
https://sapling.ai/comparison/onprem. Sapling deployments can also be configured for no data retention, sacrificing some model customization.
Cost-wise, it doesn't make sense for individuals to host a neural-network based grammar checker, though some of the rule-based options may work. There's a future where if we can maintain some sort of Moore's law scaling we will be able to run these language models on individual computers as opposed to the cloud.