Pairing Single Quotes

During pentest, I came across an interesting and unusual case where developers're trying to escape a single quote (') via a single quote (') in an script context. Further, I noticed that they were adding ' on the right hand side of the injected single quote. The developers're trying to have single quotes in pair but why? Are they trying to escape or something else? It sounds unfortunately funny and at the same time shows XSSing is not going anywhere in the near future.

The screen-shot given below shows the reflection of our interest. Please keep in mind that I had used the harmless XSS probe string i.e., "xxxxxxxx'yyyyy. The < sign is not part of probe string given site has enabled .NET's XSS protection. The site forcefully redirects me to an error page if I inject < character. 

It can be seen in the screen-shot above that site has added or appended an extra ' for escaping (the apparent reason I can think of) a single quote from the probe string. As you could aware of the fact that \ may be used as an escape character for ' and " quotes in an script context like \' and \" respectively. The site was adding/appending an extra ' as an escape character for the injected ' so payload(s) like '-confirm(1)-' and ');confirm(1);// do not work. Soon I realized during testing that \ is not escaped or controlled or filtered. The attack payload I used to XSS this case is: \');confirm(1);//. It starts with \'.  The screen-shot is given below and later I will explain why the payload works.

The attack payload was \');confirm(1);//. It starts with \' in order to make single quote as an escape character. After that application has added/appended one single quote because application developers want to have or see single quotes in pair. So we have a situation like this: '\''. It is perfectly legit given in a pair of single quotes there is an escaped single quote. After that ) character closes the function call prematurely followed by a semi-colon i.e., ; as a statement terminator. The next is a proof of concept JavaScript function call i.e., confirm(1); followed a single line comment i.e., // in order to avoid syntax error or neutralizes the effect of remaining parts of function call i.e., notyAlert. This XSS shows how one can leverage application's unusual functionality against it.