If the opposite were true and the government proposes spending $1 trillion on infrastructure spending we will see a shift outward of the demand curve and rates will tick upward to a new equilibrium point. The crowding out occurs when we have movement along the demand curve (from the old interest rate --> new demand curve intersection up to the new intersection of the S and D curve).
With a decrease in government spending your demand curve for the loan-able funds market will shift inward and push the interest rate lower. When a fall in the interest rate leads to higher investment spending, the resulting increase in real GDP generates exactly enough additional savings to match the rise in investment spending.
It is somewhat agreed upon that contractionary fiscal policy leads to a surplus and the government can act as a creditor rather than a debtor. It will also leave more money for private investments for people such as small borrowers.
(There are some economists that believe that under the right circumstances that expansionary government policies may produce crowing in instead of crowding out. Keynesian economists may suggest that if the policy is strong enough to change the economic climate then businesses may find it profitable to add capacity -induced investment- which works to counteract and possibly out weigh the crowding out effect.)