My one t (the one I saw for a year recently) would do email where I would write if I needed to just get something away from me (usually extreme frustration or anger at therapy) and sometimes she would write back or sometimes I would tell her not to. The purpose for me was to get it away from me, not so much to get a response from her. A couple of times I asked for specific reassurance that therapy was proceeding as it should and she did usually manage to do that okay. She also said I could ask for extra appointments if I wanted. I did that once when I was in an extremely agitated state and needed to be much less so for a specific purpose later that day. That was the one time I remember I left feeling actually better than when I went in.
The second one (for nine months recently) gave out her telephone number and said to call if I had a certain couple of things occur. I tried it twice. I never felt like it was all that useful because by then the situation was over and I had moved on and it felt silly to talk about it like a crisis.

Both of mine were always fairly encouraging to me - I think mostly because they thought I need to depend on others rather than I am too dependent. Always withdrawing rather than going towards them.

I think to become less dependent you could try to distract yourself with activities with friends or sports or something like that to get you out of house and out doing something where contacting the t would not be as easy. I think they sort of expect dependency from clients. May I ask why you want less dependency at this point? Has t said something or are you feeling odd about it?