Hi, even if it is a family issue, you should have approached HR; they might have provided you with some suggestions. Have they given you training using licensed software?
It depends on the company. Some may follow procedures vigorously, while some companies, to close the file, will send you some communications and then close the file.
Now, you have two options. Talk to HR and explain that due to some health issues, you are not in a position to continue. You can communicate verbally or through a registered post acknowledgment due (RPAD) letter. You will also need some medical proof.
Even if the company files a civil case, they need to prove in court the money incurred by them towards training you.
Hope you have not submitted any security cheque (undated) with them. If so, they will deposit the cheque, and after it is dishonored, they will file a criminal case against you. This is very important.
In the worst case, if you change your address, all communications will bounce back to them, and they will close the file. I'm not supposed to suggest this option, but I have seen cases like this recently.