I think the easiest way to achieve this is to create a World Space FFD-modifier (Free Form Deformation) around your object and adjust it to simulate a flat tire. The world space modifiers are found under Create > Spacewarps > Geometric/Deformable > FFD.
It’s important you use a world space modifier for this, as opposed to the sub object modifiers you find under the Modify panel.
If you still need to work with sub object modifiers for this there is a way using Script Controllers to make the modifier gizmo respond and inversely transform to any change made to the node’s transform to “lock” it in place.
[li]For this you need a control object, such as a point or dummy helper. What kind of object you use doesn’t matter as long as it has a transform of it’s own.
[/li][li]Apply a sub object modifier to the object you wish to deform.
[/li][li]Open up the curve editor, find your object and the modifier you want to “lock”.
[/li][li]Expand the modifier tree in the curve editor so you see the Gizmo : Position/Rotation/Scale branch.
[/li][li]Right-click on it and select Assign Controller.
[/li][li]Assign Transform Script.
[/li][li]Edit the properties of the newly assigned script controller.
[/li][li]Create two variables inside the controller, and by clicking Assign Node point one variable to the main node of the object you want to deform, and one pointing to the main node of the control object (the helper object).
[/li][li]Then write the following expression (thisObj = the object containing the modifier) (thatObj = the helper object.)
thatObj.transform *inverse thisObj.objectTransform
Now you are able to control the sub object gizmo using the world based helper object, which means that if you rotate the deformed object the modifier gizmo will always stay locked in place as long as the helper object doesn’t move.