Hello,
Everyone of us have some or other genuine reasons to terminate or end our employment.
I can very well understand your situation that since your mom (or any of your family members for that matter) are called ill majorly and you are not in same town to adjust with the situation.
However, while you resigned, what reason did you state in your resignation letter?
Another thing is, at times we do not feel the need to communicate on whole or we just take it for granted.
Like you mentioned that your company has a 1 month notice policy and as a result, perhaps you never mentioned your last working day or relieving with immediate effect. (Excuse me if I am wrong here and if you mentioned the same, I am generalizing as most of us do not mention this over resignation)
The reason I stated this is because when someone puts the paper down, as an employer one thinks you must have got better opportunity and now you just want to rush to it. It is very natural to think that way, we are human and we can't control our feelings.
Now coming to the solution part. Write again to the employer that you resigned on account of poor health of your mother and when it was getting too serious you had to but leave. Just say in the tension you just couldn't do the proper exit formalities, but you do not intend to abscond or run away. Mention that you are open to discussion and negotiation if possible and you can scan them your mother's report to prove the genuineness of case. Add that you understand that since you have served only 5 days you are liable to paying of remaining 25 days' salary and mention that you would yourself come down for a full and final settlement and relieving cum experience letter as soon as your mother's condition is somewhat normal. Try to convince them that since you worked in a different city than your hometown it is not possible to handle both situation together.
Add that you would be obliged if they can consider your application as special case and can relieve you on shorter notice so that you are not burdened up with higher payment.
The key is convincing and only convincing. Possibly they may just get annoyed, and try to just think if you had been in their place, perhaps you too might have thought why didn't he inform me before.... It is just human nature. I do understand your concern that they should as well try to understand your situation but that is possible only if try to explain this to them again and again without losing patience.
Patience can solve complex problems. All the best.