We are using Lime Survey to gether student data for a particular administrative process which has multiple events for a student may not be set up in our IT systems yet. The survey needs to be public since our office does not get a list of all students (ie no upload survey participant list initially). 

The use case is that a student makes a submission or a partial submission and would need to be able to come back and update their survey either before clicking submit or after clicking submit. This would seem to imply using tokens. But the student may need to submit a completely new instance of the previous survey for a different event. So, a student could actually have 2 or more responses and need to be able to go back and update a particular survey.

Is this possible? If yes, what are the settings?

No. At least not without quite a lot of custom coding, I think.

For tokens you need a token table, if you do not have the students contact, you can't create a token for them, obviously.

You might look into public registration, but I don't think that Limesurvey is the ideal tool for what you are trying to do.

Like most survey systems, Limesurvey is not the best fit for going back into the data and update. Most survey systems are made to complete a survey and that is it. If tokens are used (or with the feature "save and resume later" you can stop in the survey, but generally there is no real "user managment" for respondents. So you won't have a login with a list of forms that you can fill. You rather get personalized access to one form.

Complex to construct, need full project description  .

But some idea.
1. 1st survey is a register survey : gitlab.com/SondagesPro/SurveyAccess/surveyRegister : user get the token to another survey, attribute are filled by value from this survey
2. 2nd survey is a token enable survey with Allow edit and Token persisentce (he can come back a lot of time)
3. The 2nd survey include a questionExtraSurvey   ( sample )

Denis