Should I not submit an assignment if I run into personal difficulties?

No. It is to your advantage to always submit a piece of work for all assessment tasks set, even if it is unfinished or incomplete. There may be serious consequences if any assignment task is missed (especially resits.)
As mentioned in another FAQ (on ‘requesting a new submission date’), if you later have a PEC application for your circumstance approved and is given an extended or defered due date, you may be permitted to submit again and have graded another replacement assignment piece instead, providing it was submitted before the approved new submission date.
Although you may feel obliged to not submit a sub-par or incomplete piece of work, you should know that a record of every attempt is kept and considered at the Board of Examination. This includes attempts where below-average grades were awarded, which are considered more favorable and may be compensatable by the board, than a non-submission attempt, which is not.

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