Hello there, @kdlight_62 ...
Sorry to see that your question has been sitting out here unanswered since late May 2020. I think the answer to your question may depend on what kind of assignment the student is completing. For example, if the assignment is to write an essay paper, those are typically done in an "offline" setting using software such as Microsoft Word to compose the essay. If your assignment uses discussion topics where students reply online, then those replies generally need to be typed while working online so they can then be posted to the topic. If the assignment were a quiz, you may be able to set it up so that students could continue where they left off...assuming that the quiz was not yet submitted to you. One additional way that your students may be able to work "online" is if you have either the Google or Office 365 integrations set up with Canvas. Using either of these, you could create a Google or O365 cloud assignment. Then, you select a file from your Google or O365 account to share with students. When the students begin to work on the assignment, they sign in to their own Google or Microsoft account. It creates a copy of your document and saves it in their own account. (Your file remains intact.) Students work on their own copy of the file you gave them, and then they submit it to you.
I hope this information will be of some help to you. If you have any other questions about this...please let Community members know...thanks! Be well.
