If you purchase a locked CELL phone that eventually becomes unlocked does the IMEI number change or how does a carrier know the difference ?Did you ask Google?
There are many r websites that will do anything to a smartphone.
For a cheap smartphone, it mat not be worth the effort.

As for the IMEI number, it is possible to change it.
..from Google:
IMEI (International MOBILE Equipment Identity) is a unique 15-digit serial number given to every mobile phone which can then be used to check information such as the phone's Country of Origin, the Manufacturer and it's Model Number. The Model Code, Serial Number and IMEI are printed at the back of the device.
Here is a guide from a a VENDOR that sells smartphones.
http://www.bestbuy.com/site/clp/why-buy-an-unlocked-phone/pcmcat284300050008.c?id=pcmcat284300050008
Quote

What is an unlocked smartphone? An unlocked smartphone is a phone that isn't tied to a specific carrier or contract. Therefore, you have the freedom to shop for the latest phones and plans as often — or as INFREQUENTLY — as you like. And when it comes to international travel, unlocked phones can't be beat.

Since unlocked phones are not tied to a specific carrier you have a greater selection of phones and features to choose from. Whether you are looking for a phone with basic calling and texting options, a smartphone with all the latest features like the Samsung Galaxy S7, or anything in between, you'll be able to find the right unlocked phone to meet your NEEDS and budget.