MacBook Air Hard drive crashed (2013 Model)
You can replace the SSD (Solid State Drive, it is not a hard drive with spinning disk)!

.... with a model from OWC yourself if you know your way around embedded hardware. 

Apple does not sell parts to individuals, but an AASP or APSP (Apple Service Providers) can replace it for you with an Apple part. 

The SSDs are not compatible with m.2 or mSATA, you have to use the specific MacBook Air SSD for your model. Major MacBook Air releases also have different SSDs due to incompatible upgrades (protocol upgrades and electrical upgrades).

Sites like iFixit have guides that can assist you with this.

See some instructions here https://everymac.com/systems/apple/macbook-air/macbook-air-faq/macbook-air-mid-2013-how-to-replace-upgrade-ssd-storage.html