Danielle,

I do not practice in the area of bankruptcy law, and there are people far more knowledgeable out there on the subject than I am. The law of bankruptcy has also undergone some significant changes twice in the past 5 or 6 years. However, I do a lot of debt collection work, and run into bankruptcies as they impact on the creditor's ability  to collect debts owed to him.

Generally there are several different classes of creditors, and each is accorded a different priority of payment depending upon the class into which he falls. The least likely to be paid is the unsecured creditor. The secured creditors such as mortgagees are accorded better treatment, and are generally paid in full to the extent that there are funds available in the bankrupt estate and the order in which they perfected their liens/mortgages/attachments. 

I have not heard of the 10 day rule. However, it may be a provision of one of the new redrafts of the bankruptcy code.
Generally there is an order of automatic stay that becomes effective at the time the bankruptcy petition is filed with the court. As of that date the secured or unsecured status of a debt is pretty much frozen. In the case of mortgages it depends on the date on which they are recorded. I have also seen mortgagees successfully obtain a relief from the automatic stay order.In which case they are free to proceed with a foreclosure which was initiated prior to the filing of the bankruptcy.
 
I am not certain as to whether you are stating that the 10 day rule applies to the mortgagee's ability to perfect the mortgage after a bankruptcy has been filed. It would seem that there would be no reason to place that requirement on the recording date if there is no bankruptcy looming on the horizon, but that does not mean that the new redrafts of the law have not altered this.

There is also something called a preferential transfer which can be reversed by the bankruptcy court if they are made within a certain time prior to the bankrupty's filing date. Perhaps the 10 day period of which you speak may relate to that under the new redrafts of the law.

You have raised a really interesting question. If there is anyone out there with an answer, I would really be interested in hearing it... all knowledgeable answers invited.