In order to play you need ability, so it's quite natural to say:
(i) I can play (soccer). (ii) I can't play (soccer) (iii) I can play soccer with a ball (iv) I can't play soccer without a ball.
Likewise it is possible to use the modal can with the verb buy
(i) I can buy. (ii) I can't buy (Note that we are speaking about the ability to buy, no object is required, sentences (i) and (ii) stand on their own feet.) (iii) I can buy food. (iv) I can buy food with money. (v) I can't buy food without money
to have no + object
- I have no money. [to do with what?]
- I have no money with which to buy [to buy what?]
- I have no money with which to buy food. [outdated]
- I have no money to buy food with. [the same meaning as 3.]
- I have no money to buy food. [grammatical]
To specify that you buy food with money is a bit tautological. Can sentence 5 stand alone? Yes, it can.
- I have no ball [to do with what?]
- I have no ball with which to play [to play what?]
- I have no ball with which to play soccer. [outdated]
- I have no ball to play soccer with. [modern]
Delete soccer and we're left with
- I have no ball to play with
In #2. which refers to ball. If the object of the sentence was friend then whom could be used.
- I have no friend with whom to play.
This is quite formal and some may find it pompous and artificial. Nowadays it is more common to hear:
- I have no friend to play with.
The preposition with refers to the friend. You play with a friend. Similarly you can play soccer with a friend. You don't play with soccer; e.g. *I play with soccer. [NO] However, you play soccer with a ball. Here with tells us that a ball is used in order to play soccer. E.g. I write with a pen. But I could also write with a pencil, biro, marker, penknife etc. If I have no pen, I say:
- *I have no pen to write [for what?]
- I have no pen to write with
In #2. the sentence sounds incomplete.
with
10. a. By the means or agency of: eat with a fork; made us laugh with his jokes.