If, as a tenant, you are liable to pay any debts to the landlord (i.e. unpaid rent, bills, damage costs) then the Guarantor is also liable and if you don’t pay the landlord will look to claim these costs from your Guarantor.
If you are a joint tenant, your guarantor can be pursued for any debts from any tenant in the property – just as the tenants are jointly and severally liable, so are the guarantors. This can seem unfair, especially, if you have paid your share and it is another tenant who hasn’t. The only way to avoid this would be if your guarantor signs a written agreement with the landlord confirming their liability is limited to a specified portion of the rent (or damage) but many landlords will not agree to this.