It is possible to change the size of Text fields in a feature class, though not other field types like Long Integer, Date, etc. To do this:
1. Open ArcCatalog.
2. Find the feature to be changed and double-click to open Esri properties.
3. Click the Fields tab and highlight the Field Name that needs to change.
4. In the Length field in Field Properties, increase the number to the desired size.
Note: To protect the integrity of data currently in the table, Text fields can be increased in size but not decreased.