Is a pic 16f877a reprogrammable
While there are some exceptions, typically the following applies:

The 'F' within the part number PIC16F877A indicates it is a flash based device and is reprogrammable using ICSP techniques.

Whereas the presence of a 'C' instead of the 'F' indicate a EPROM based device which are typically One Time Programmable (OTP) devices. However, some 'C' models do provide UV erasure window which allows the device to be erased using UV light and reprogrammable once erased.

There are also 'CR' and 'CE' variants, the 'CR' type indicates a factory preprogrammed ROM device and the 'CE' indicates a 'C' type combined with an EEPROM.