I've been natural for about 2 years and 6 months and I did not do a big chop or a small chop either. This was not wise at all. I never cut the relaxed ends off of my hair which resulted in breakage. IMO it is important to eventually cut these ends off. You don't necessarily have to do a big chop but I think the sooner you cut them off the better. There are many ladies on here who successfully managed growing out their natural hair w/o the big chop but they usually eventually cut off those ends and are great at maintaing two textures.
I thought I knew how to manage my 4a/b hair combined with the relaxed ends but I was wrong. I tried to transition using braidouts, braids, flatironing and buns. Unfortunately, those relaxed ends did break off. Flatironing worked the best I'd say because I simply wrapped the hair and did very little manipulation. You still have to be careful though..On a happier note, it can be done successfully you just have to be extrememly careful and pay attention to the different needs of the two textures.
