In all of the start conditions, students have access to the test indefinitely once it is published or after the scheduled date/time. Therefore it is always advisable to close the test once you have received all the submissions. To close the access to a test, click on the published button on the top-right and choose 'Close'. Once the test has been closed, no student would be able to start the test.
Please note that students who have started an assessment will be able to continue writing even if the teacher closes the assessment. But all submissions received after the test is closed would be marked as 'Late submissions and their submission date and time would be highlighted in red color.