This is widely misunderstood.
There is a hard limit to the number of bitshares: 3,600,566,000 (3.6 billion)
In circulation today are 2,571,040,000 BTS with 1,029,526,570 BTS yet to come in to circulation.
The 1,029,526,570 BTS that is yet to come into circulation is known as the reserve pool.
With bitcoin, there are 16 million Bitcoin in circulation today, with 5 million that will be mined in the future.
The miners are paid in new bitcoin that is entering circulation at a fixed rate to reward them to keep the network secure.
Bitshares doesn't have miners. But it does introduce new BTS into circulation at a maximum % rate of the pool, currently:
14,670 per hour
352,080 per day
2,464,560 per week
10,597,608 per month
12.5 % (1800 per hour) of this is automatically given to the witnesses who are elected individuals that help secure the bitshares network.
The rest can be given out to anyone that requests it but only with approval.
Approval is given by BTS owners by voting on these requests called "Worker Proposals."
If BTS owners do not approve any requests then the BTS just stay in the reserve pool.
The requests that do get approval are usually those that are improving the bitshares software.
Looking at the graph above you can see that over time more BTS is leaving the reserve pool and entering circulation to pay our witnesses and worker proposals.
However, this is not just a one way flow.
Every transaction that happens on the bitshares network has a small fee ( http://cryptofresh.com/fees )and this fee goes in to the reserve pool.
If the number of transactions happening on the bitshares was generating more BTS in fees than the reserve pool was adding to circulation the reserve pool balance would go up instead of down.