They'll send a letter but they won't be hunting down and demanding evidence from someone who sold £1100 worth of stuff and claims it was just personal possessions unless it's blindingly obvious they're lying, it just wouldn't be worth the effort.
I don't know. It's very little effort on their part to send you a letter asking to provide evidence. The onus to prove is on you. Can't prove it? Sorry, it's not the justice system where innocent until proven guilty. It's guilty unless you manage to prove innocent, isn't it?
My girlfriend did self-assessment because worked at two jobs, was hoping that she overpayed tax, so hoping to get some back. Declared a few work expenses to be reimbursed (like a uniform or something). Instead of getting a reimbursement, she received a letter saying that she claimed too many work expenses and now she owes money to the Queen, even though she literally did anything about said work expenses after the tax year ended, so she didn't apply for anything prior and didn't get any discounts or anything. So they somehow weirdly managed to turn it around and make it so that she owes 160 quid. Which is, ok - survivable, just pay and get on with your life, and lesson learned: don't submit self-assessment if you don't have to.
But the point is: you think they'd have gotten off her back? The letter clearly said she had something like 60 days to dispute and had to pay by the end of year. Should she have thrown the letter away and forgotten about it?